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375_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 4 as the base:
Step 1: Fold face 2 upwards
Step 2: Fold face 1 downwards
Step 3: Fold face 3 upwards towards face 1
Step 4: Fold face 6 downwards towards face 3
Step 5: Fold face 5 downwards towards face 3
Based on the above steps, can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=4)", "faces": {"3": [[0.9999999999999999, 1.0, 1.0], [1.0, 1.0, 0.0], [1.0, 2.0, 0.0], [0.9999999999999999, 2.0, 1.0]], "4": [[1, 1, 0], [2, 1, 0], [2, 2, 0], [1, 2, 0]], "2": [[2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [2.0, 2.0, 0.0]], "1": [[2.0, 1.0, 1.0], [1.0, 1.0, 1.0], [1.0, 2.0, 1.0], [2.0, 2.0, 1.0]], "6": [[1.0, 1.0, 1.0], [0.9999999999999997, 1.0, 0.0], [0.9999999999999997, 2.0, 0.0], [1.0, 2.0, 1.0]], "5": [[2.0, 0.9999999999999999, 0.9999999999999997], [1.9999999999999996, 0.9999999999999999, -4.440892098500626e-16], [0.9999999999999997, 1.0, 0.0], [1.0, 1.0, 1.0]]}, "face_connections": {"3": ["4"], "4": ["3", "2"], "2": ["4", "1"], "1": ["2", "6"], "6": ["1", "5"], "5": ["6"]}, "valid": false}, "base_face": "4", "folding_steps": [["2", "4", [2, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["1", "2", [2.0, 1.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["3", "4", [1, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["6", "1", [1.0, 1.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["5", "6", [1.0, 1.0, 1.0], [-3.3306690738754696e-16, 0.0, -1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 1 downwards", "Fold face 3 upwards towards face 1", "Fold face 6 downwards towards face 3", "Fold face 5 downwards towards face 3"], "images_per_step": ["output_dir/folding_nets/random2_net17_base4_step1.png", "output_dir/folding_nets/random2_net17_base4_step2.png", "output_dir/folding_nets/random2_net17_base4_step3.png"], "id": "random2_net17_base4"} | q+steps | [
"no",
"yes"
] |
|
369_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 3 as the base:
Step 1: Fold face 4 upwards
Step 2: Fold face 2 inwards towards face 3
Step 3: Fold face 5 inwards towards face 3
Step 4: Fold face 6 downwards towards face 4
Step 5: Fold face 1 downwards towards face 3
Based on the above steps, can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "1-3-2 Net", "faces": {"3": [[0, 2, 0], [1, 2, 0], [1, 3, 0], [0, 3, 0]], "4": [[1.0, 2.0, 0.0], [1.0, 2.0, 1.0], [1.0, 3.0, 1.0], [1.0, 3.0, 0.0]], "2": [[0.0, 2.0, 0.0], [0.0, 2.0, 1.0], [1.0, 2.0, 1.0], [1.0, 2.0, 0.0]], "5": [[-2.83276944882399e-16, 3.0, 0.0], [-2.83276944882399e-16, 3.0, 1.0], [0.0, 2.0, 1.0], [0.0, 2.0, 0.0]], "6": [[-2.83276944882399e-16, 3.0, 1.0], [0.9999999999999997, 3.0000000000000004, 1.0000000000000002], [0.9999999999999999, 2.0000000000000004, 1.0000000000000002], [-4.930380657631324e-32, 2.0, 1.0]], "1": [[9.957992501029601e-17, 3.0, 0.0], [1.0000000000000002, 3.0000000000000004, 6.661338147750939e-16], [0.9999999999999997, 3.0000000000000004, 1.0000000000000002], [-2.83276944882399e-16, 3.0, 1.0]]}, "face_connections": {"3": ["4"], "4": ["3", "2"], "2": ["4", "5"], "5": ["2", "6"], "6": ["5", "1"], "1": ["6"]}, "valid": true}, "base_face": "3", "folding_steps": [["4", "3", [1, 2, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["2", "4", [1.0, 2.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["5", "2", [0.0, 2.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["6", "5", [-2.83276944882399e-16, 3.0, 1.0], [2.83276944882399e-16, -1.0, 0.0], -1.5707963267948966], ["1", "6", [-2.83276944882399e-16, 3.0, 1.0], [1.0, 4.440892098500626e-16, 2.220446049250313e-16], -1.5707963267948966]], "folding_step_descs": ["Fold face 4 upwards", "Fold face 2 inwards towards face 3", "Fold face 5 inwards towards face 3", "Fold face 6 downwards towards face 4", "Fold face 1 downwards towards face 3"], "images_per_step": ["output_dir/folding_nets/random2_net9_base3_step1.png", "output_dir/folding_nets/random2_net9_base3_step2.png", "output_dir/folding_nets/random2_net9_base3_step3.png", "output_dir/folding_nets/random2_net9_base3_step4.png", "output_dir/folding_nets/random2_net9_base3_step5.png", "output_dir/folding_nets/random2_net9_base3_step6.png"], "id": "random2_net9_base3"} | q+steps | [
"yes",
"no"
] |
|
431_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 4 as the base:
Step 1: Fold face 2 upwards
Step 2: Fold face 3 upwards towards face 2
Step 3: Fold face 5 downwards towards face 2
Step 4: Fold face 6 upwards towards face 5
Step 5: Fold face 1 inwards towards face 2
Based on the above steps, can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "1-3-2 Net", "faces": {"2": [[0.9999999999999999, 0.0, 1.0], [1.0, 0.0, 0.0], [1.0, 1.0, 0.0], [0.9999999999999999, 1.0, 1.0]], "5": [[1.0, 1.0, 1.0], [2.0, 1.0, 1.0], [2.0, 0.0, 1.0000000000000002], [1.0, 0.0, 1.0000000000000002]], "3": [[1.0, 1.0, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [1.0, 1.0, 1.0]], "4": [[1, 0, 0], [2, 0, 0], [2, 1, 0], [1, 1, 0]], "6": [[2.0, 0.0, 0.0], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [2.0, 1.0, 0.0]], "1": [[1.0, -6.123233995736766e-17, 0.0], [1.0, -6.123233995736766e-17, 1.0], [2.0, 0.0, 1.0], [2.0, 0.0, 0.0]]}, "face_connections": {"2": ["4"], "5": ["3"], "3": ["5", "4"], "4": ["2", "3", "6"], "6": ["4", "1"], "1": ["6"]}, "valid": true}, "base_face": "4", "folding_steps": [["2", "4", [1, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "4", [2, 1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["5", "3", [2.0, 1.0, 1.0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["6", "4", [2, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["1", "6", [2.0, 0.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 3 upwards towards face 2", "Fold face 5 downwards towards face 2", "Fold face 6 upwards towards face 5", "Fold face 1 inwards towards face 2"], "images_per_step": ["output_dir/folding_nets/random2_net11_base4_step1.png", "output_dir/folding_nets/random2_net11_base4_step2.png", "output_dir/folding_nets/random2_net11_base4_step3.png", "output_dir/folding_nets/random2_net11_base4_step4.png", "output_dir/folding_nets/random2_net11_base4_step5.png", "output_dir/folding_nets/random2_net11_base4_step6.png"], "id": "random2_net11_base4"} | q+steps | [
"no",
"yes"
] |
|
44_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 6 as the base:
Step 1: Fold face 5 upwards
Step 2: Fold face 4 inwards towards face 6
Step 3: Fold face 3 downwards towards face 5
Step 4: Fold face 2 downwards towards face 5
Step 5: Fold face 1 downwards towards face 2
Based on the above steps, can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "1-3-2 Net", "faces": {"1": [[2.0, -1.0000000000000002, 0.0], [2.0, -0.9999999999999999, 1.0], [3.0, -0.9999999999999999, 1.0], [3.0, -1.0000000000000002, 1.1102230246251565e-16]], "2": [[3.0, -0.9999999999999999, 1.0], [3.0, 1.224646799147353e-16, 1.0], [3.0000000000000004, 1.8369701987210294e-16, 0.0], [3.0000000000000004, -0.9999999999999998, 0.0]], "3": [[2.0, -0.9999999999999999, 1.0], [2.0, 6.123233995736765e-17, 1.0], [3.0, 1.224646799147353e-16, 1.0], [3.0, -0.9999999999999999, 1.0]], "4": [[2.0, -1.0, 6.123233995736766e-17], [2.0, 0.0, 0.0], [2.0, 6.123233995736765e-17, 1.0], [2.0, -0.9999999999999999, 1.0]], "5": [[2.0, 0.0, 0.0], [3.0, 0.0, 0.0], [3.0, 6.123233995736766e-17, 1.0], [2.0, 6.123233995736766e-17, 1.0]], "6": [[2, -1, 0], [3, -1, 0], [3, 0, 0], [2, 0, 0]]}, "face_connections": {"1": ["3"], "2": ["3"], "3": ["1", "2", "4"], "4": ["3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": true}, "base_face": "6", "folding_steps": [["5", "6", [3, 0, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["4", "5", [2.0, 0.0, 0.0], [0.0, 6.123233995736766e-17, 1.0], 1.5707963267948966], ["3", "4", [2.0, 6.123233995736765e-17, 1.0], [0.0, -1.0, 0.0], -1.5707963267948966], ["2", "3", [3.0, 1.224646799147353e-16, 1.0], [0.0, -1.0, 0.0], -1.5707963267948966], ["1", "3", [2.0, -0.9999999999999999, 1.0], [1.0, 0.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 5 upwards", "Fold face 4 inwards towards face 6", "Fold face 3 downwards towards face 5", "Fold face 2 downwards towards face 5", "Fold face 1 downwards towards face 2"], "images_per_step": ["output_dir/folding_nets/net10_base6_step1.png", "output_dir/folding_nets/net10_base6_step2.png", "output_dir/folding_nets/net10_base6_step3.png", "output_dir/folding_nets/net10_base6_step4.png", "output_dir/folding_nets/net10_base6_step5.png", "output_dir/folding_nets/net10_base6_step6.png"], "id": "net10_base6"} | q+steps | [
"no",
"yes"
] |
|
446_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=1)", "faces": {"5": [[0.9999999999999999, 0.0, 0.0], [1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [0.9999999999999999, 0.0, 1.0]], "6": [[1.0, 1.0, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [1.0, 1.0, 1.0]], "2": [[2.0, 1.0, 0.0], [2.0, 0.0, 0.0], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0]], "4": [[2.0, 0.0, 0.0], [1.0, -6.123233995736766e-17, 0.0], [1.0, -6.123233995736766e-17, 1.0], [2.0, 0.0, 1.0]], "1": [[1.0, -6.123233995736766e-17, 0.0], [0.9999999999999999, 0.9999999999999999, 0.0], [0.9999999999999999, 0.9999999999999999, 1.0], [1.0, -6.123233995736766e-17, 1.0]], "3": [[1, 0, 0], [2, 0, 0], [2, 1, 0], [1, 1, 0]]}, "face_connections": {"5": ["6"], "6": ["5", "2", "3"], "2": ["6", "4"], "4": ["2", "1"], "1": ["4"], "3": ["6"]}, "valid": false}, "base_face": "3", "folding_steps": [["6", "3", [2, 1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["5", "6", [1.0, 1.0, 0.0], [0.0, 0.0, 1.0], 1.5707963267948966], ["2", "6", [2.0, 1.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["4", "2", [2.0, 0.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["1", "4", [1.0, -6.123233995736766e-17, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 5 inwards towards face 3", "Fold face 2 inwards towards face 3", "Fold face 4 inwards towards face 5", "Fold face 1 inwards towards face 5"], "images_per_step": ["output_dir/folding_nets/random2_net14_base3_step1.png", "output_dir/folding_nets/random2_net14_base3_step2.png", "output_dir/folding_nets/random2_net14_base3_step3.png", "output_dir/folding_nets/random2_net14_base3_step4.png"], "id": "random2_net14_base3"} | q_only | [
"yes",
"no"
] |
|
70_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 6 as the base:
Step 1: Fold face 2 upwards
Step 2: Fold face 5 inwards towards face 6
Step 3: Fold face 1 downwards towards face 5
Step 4: Fold face 4 upwards towards face 2
Step 5: Fold face 3 downwards towards face 4
Based on the above steps, can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "Big T - Variant 1", "faces": {"4": [[0.9999999999999999, 0.0, 1.0], [1.0, 0.0, 0.0], [1.0, 1.0, 0.0], [0.9999999999999999, 1.0, 1.0]], "6": [[1, 0, 0], [2, 0, 0], [2, 1, 0], [1, 1, 0]], "5": [[2.0, -6.123233995736766e-17, 1.0], [2.0, 0.9999999999999999, 1.0], [2.0, 0.9999999999999999, 1.1102230246251565e-16], [2.0, -1.232595164407831e-32, 0.0]], "2": [[1.0, -6.123233995736766e-17, 1.0], [2.0, -6.123233995736766e-17, 1.0], [2.0, 0.0, 0.0], [1.0, 0.0, 0.0]], "1": [[1.0, 0.9999999999999999, 1.0000000000000002], [2.0, 0.9999999999999999, 1.0000000000000002], [2.0, -6.123233995736766e-17, 1.0], [1.0, -6.123233995736766e-17, 1.0]], "3": [[1.0, 1.0, 2.220446049250313e-16], [2.0, 1.0, 2.220446049250313e-16], [2.0, 0.9999999999999999, 1.0000000000000002], [1.0, 0.9999999999999999, 1.0000000000000002]]}, "face_connections": {"4": ["6"], "6": ["4", "2"], "5": ["2"], "2": ["6", "5", "1"], "1": ["2", "3"], "3": ["1"]}, "valid": true}, "base_face": "6", "folding_steps": [["2", "6", [1, 0, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["5", "2", [2.0, -6.123233995736766e-17, 1.0], [0.0, 6.123233995736766e-17, -1.0], -1.5707963267948966], ["1", "2", [1.0, -6.123233995736766e-17, 1.0], [1.0, 0.0, 0.0], -1.5707963267948966], ["4", "6", [1, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "1", [1.0, 0.9999999999999999, 1.0000000000000002], [1.0, 0.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 5 inwards towards face 6", "Fold face 1 downwards towards face 5", "Fold face 4 upwards towards face 2", "Fold face 3 downwards towards face 4"], "images_per_step": ["output_dir/folding_nets/random1_net4_base6_step1.png", "output_dir/folding_nets/random1_net4_base6_step2.png", "output_dir/folding_nets/random1_net4_base6_step3.png", "output_dir/folding_nets/random1_net4_base6_step4.png", "output_dir/folding_nets/random1_net4_base6_step5.png", "output_dir/folding_nets/random1_net4_base6_step6.png"], "id": "random1_net4_base6"} | q+steps | [
"no",
"yes"
] |
|
345_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 6 as the base:
Step 1: Fold face 2 upwards
Step 2: Fold face 4 inwards towards face 6
Step 3: Fold face 5 downwards towards face 6
Step 4: Fold face 3 downwards towards face 5
Step 5: Fold face 1 downwards towards face 5
Based on the above steps, can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "1-3-2 Net", "faces": {"5": [[3.0, -1.0000000000000002, 1.1442377452219691e-17], [2.0, -1.0, 6.123233995736766e-17], [2.0, -0.9999999999999999, 1.0], [3.0, -1.0000000000000002, 1.0000000000000002]], "1": [[3.0, -0.9999999999999999, 1.0], [3.0, 1.224646799147353e-16, 1.0], [3.0000000000000004, 1.8369701987210294e-16, 0.0], [3.0000000000000004, -0.9999999999999998, 0.0]], "3": [[2.0, -0.9999999999999999, 1.0], [2.0, 6.123233995736765e-17, 1.0], [3.0, 1.224646799147353e-16, 1.0], [3.0, -0.9999999999999999, 1.0]], "4": [[2.0, -1.0, 6.123233995736766e-17], [2.0, 0.0, 0.0], [2.0, 6.123233995736765e-17, 1.0], [2.0, -0.9999999999999999, 1.0]], "2": [[2.0, 0.0, 0.0], [3.0, 0.0, 0.0], [3.0, 6.123233995736766e-17, 1.0], [2.0, 6.123233995736766e-17, 1.0]], "6": [[2, -1, 0], [3, -1, 0], [3, 0, 0], [2, 0, 0]]}, "face_connections": {"5": ["4"], "1": ["3"], "3": ["1", "4"], "4": ["5", "3", "2"], "2": ["4", "6"], "6": ["2"]}, "valid": true}, "base_face": "6", "folding_steps": [["2", "6", [3, 0, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["4", "2", [2.0, 0.0, 0.0], [0.0, 6.123233995736766e-17, 1.0], 1.5707963267948966], ["5", "4", [2.0, -1.0, 6.123233995736766e-17], [0.0, 1.1102230246251568e-16, 1.0], 1.5707963267948966], ["3", "4", [2.0, 6.123233995736765e-17, 1.0], [0.0, -1.0, 0.0], -1.5707963267948966], ["1", "3", [3.0, 1.224646799147353e-16, 1.0], [0.0, -1.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 4 inwards towards face 6", "Fold face 5 downwards towards face 6", "Fold face 3 downwards towards face 5", "Fold face 1 downwards towards face 5"], "images_per_step": ["output_dir/folding_nets/random3_net11_base6_step1.png", "output_dir/folding_nets/random3_net11_base6_step2.png", "output_dir/folding_nets/random3_net11_base6_step3.png", "output_dir/folding_nets/random3_net11_base6_step4.png", "output_dir/folding_nets/random3_net11_base6_step5.png", "output_dir/folding_nets/random3_net11_base6_step6.png"], "id": "random3_net11_base6"} | q+steps | [
"yes",
"no"
] |
|
231_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "Big T Net", "faces": {"3": [[0.9999999999999999, -0.9999999999999999, 0.0], [1.0, -0.9999999999999999, 1.0], [1.0, -2.0, 1.0], [0.9999999999999999, -2.0, 0.0]], "4": [[1.0, -0.9999999999999999, 1.0], [2.0, -0.9999999999999999, 1.0], [2.0, -2.0, 1.0], [1.0, -2.0, 1.0]], "1": [[2.0, -0.9999999999999999, 1.0], [2.0, -0.9999999999999999, 0.0], [2.0, -2.0, 0.0], [2.0, -2.0, 1.0]], "2": [[1.0, -1.0, 0.0], [2.0, -1.0, 0.0], [2.0, -0.9999999999999999, 1.0], [1.0, -0.9999999999999999, 1.0]], "6": [[1, -2, 0], [2, -2, 0], [2, -1, 0], [1, -1, 0]], "5": [[1.0, -2.0, 1.0], [2.0, -2.0, 1.0], [2.0, -2.0, 0.0], [1.0, -2.0, 0.0]]}, "face_connections": {"3": ["4"], "4": ["3", "1", "2"], "1": ["4"], "2": ["4", "6"], "6": ["2", "5"], "5": ["6"]}, "valid": true}, "base_face": "6", "folding_steps": [["5", "6", [1, -2, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["2", "6", [2, -1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["4", "2", [2.0, -0.9999999999999999, 1.0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["1", "4", [2.0, -0.9999999999999999, 1.0], [0.0, -1.0, 0.0], -1.5707963267948966], ["3", "4", [1.0, -0.9999999999999999, 1.0], [0.0, -1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 5 upwards", "Fold face 2 upwards", "Fold face 4 downwards towards face 5", "Fold face 1 downwards towards face 2", "Fold face 3 downwards towards face 2"], "images_per_step": ["output_dir/folding_nets/random1_net3_base6_step1.png", "output_dir/folding_nets/random1_net3_base6_step2.png", "output_dir/folding_nets/random1_net3_base6_step3.png", "output_dir/folding_nets/random1_net3_base6_step4.png", "output_dir/folding_nets/random1_net3_base6_step5.png", "output_dir/folding_nets/random1_net3_base6_step6.png"], "id": "random1_net3_base6"} | q_only | [
"yes",
"no"
] |
|
119_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 2 as the base:
Step 1: Fold face 5 upwards
Step 2: Fold face 4 inwards towards face 2
Step 3: Fold face 3 upwards towards face 5
Step 4: Fold face 6 inwards towards face 4
Step 5: Fold face 1 inwards towards face 2
Based on the above steps, can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "invalid_F", "faces": {"1": [[3.0, -2.83276944882399e-16, 0.0], [2.0, 0.0, 0.0], [2.0, 0.0, 1.0], [3.0, -2.83276944882399e-16, 1.0]], "6": [[2.0, 0.0, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [2.0, 0.0, 1.0]], "3": [[2.0, 1.0, 0.0], [3.0, 1.0, 0.0], [3.0, 1.0, 1.0], [2.0, 1.0, 1.0]], "4": [[3.0, 1.0, 0.0], [3.0, 1.0, 1.0], [2.0, 1.0, 1.0], [2.0, 1.0, 0.0]], "2": [[2, 0, 0], [3, 0, 0], [3, 1, 0], [2, 1, 0]], "5": [[3.0, 0.0, 0.0], [3.0, 0.0, 1.0], [3.0, 1.0, 1.0], [3.0, 1.0, 0.0]]}, "face_connections": {"1": ["6"], "6": ["1", "3"], "3": ["6", "4", "2"], "4": ["3", "5"], "2": ["3", "5"], "5": ["4", "2"]}, "valid": false}, "base_face": "2", "folding_steps": [["5", "2", [3, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "5", [3.0, 1.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["3", "4", [3.0, 1.0, 0.0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["6", "3", [2.0, 1.0, 0.0], [0.0, 0.0, 1.0], 1.5707963267948966], ["1", "6", [2.0, 0.0, 0.0], [0.0, 0.0, 1.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 5 upwards", "Fold face 4 inwards towards face 2", "Fold face 3 upwards towards face 5", "Fold face 6 inwards towards face 4", "Fold face 1 inwards towards face 2"], "images_per_step": ["output_dir/folding_nets/random3_net21_base2_step1.png", "output_dir/folding_nets/random3_net21_base2_step2.png", "output_dir/folding_nets/random3_net21_base2_step3.png"], "id": "random3_net21_base2"} | q+steps | [
"no",
"yes"
] |
|
72_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 1 as the base:
Step 1: Fold face 5 upwards
Step 2: Fold face 4 downwards
Step 3: Fold face 3 upwards towards face 4
Step 4: Fold face 2 inwards towards face 4
Step 5: Fold face 6 upwards towards face 4
Based on the above steps, can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "1-3-2 Net", "faces": {"6": [[0.9999999999999999, 0.0, 1.0], [1.0, 0.0, 0.0], [1.0, 1.0, 0.0], [0.9999999999999999, 1.0, 1.0]], "4": [[1.0, 1.0, 1.0], [2.0, 1.0, 1.0], [2.0, 0.0, 1.0000000000000002], [1.0, 0.0, 1.0000000000000002]], "5": [[1.0, 1.0, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [1.0, 1.0, 1.0]], "1": [[1, 0, 0], [2, 0, 0], [2, 1, 0], [1, 1, 0]], "3": [[2.0, 0.0, 0.0], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [2.0, 1.0, 0.0]], "2": [[1.0, -6.123233995736766e-17, 0.0], [1.0, -6.123233995736766e-17, 1.0], [2.0, 0.0, 1.0], [2.0, 0.0, 0.0]]}, "face_connections": {"6": ["1"], "4": ["5"], "5": ["4", "1"], "1": ["6", "5", "3"], "3": ["1", "2"], "2": ["3"]}, "valid": true}, "base_face": "1", "folding_steps": [["5", "1", [2, 1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["4", "5", [2.0, 1.0, 1.0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["3", "1", [2, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["2", "3", [2.0, 0.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["6", "1", [1, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 5 upwards", "Fold face 4 downwards", "Fold face 3 upwards towards face 4", "Fold face 2 inwards towards face 4", "Fold face 6 upwards towards face 4"], "images_per_step": ["output_dir/folding_nets/random1_net11_base1_step1.png", "output_dir/folding_nets/random1_net11_base1_step2.png", "output_dir/folding_nets/random1_net11_base1_step3.png", "output_dir/folding_nets/random1_net11_base1_step4.png", "output_dir/folding_nets/random1_net11_base1_step5.png", "output_dir/folding_nets/random1_net11_base1_step6.png"], "id": "random1_net11_base1"} | q+steps | [
"no",
"yes"
] |
|
146_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 1 as the base:
Step 1: Fold face 6 upwards
Step 2: Fold face 3 downwards
Step 3: Fold face 2 downwards towards face 1
Step 4: Fold face 5 downwards towards face 1
Step 5: Fold face 4 downwards towards face 6
Based on the above steps, can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "invalid_F", "faces": {"1": [[0, 1, 0], [1, 1, 0], [1, 2, 0], [0, 2, 0]], "6": [[1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [1.0, 2.0, 1.0], [1.0, 2.0, 0.0]], "3": [[1.0, 1.0, 1.0], [0.0, 1.0, 1.0000000000000002], [0.0, 2.0, 1.0000000000000002], [1.0, 2.0, 1.0]], "4": [[0.0, 1.0, 1.0000000000000002], [-2.220446049250313e-16, 2.0, 1.0000000000000002], [0.9999999999999998, 2.0, 1.0000000000000002], [0.9999999999999998, 1.0, 1.0000000000000002]], "2": [[0.9999999999999998, 0.9999999999999999, 0.0], [-2.220446049250313e-16, 0.9999999999999999, 2.220446049250313e-16], [0.0, 1.0, 1.0000000000000002], [1.0, 1.0, 1.0]], "5": [[-2.220446049250313e-16, 0.9999999999999999, 2.220446049250313e-16], [-2.83276944882399e-16, 1.9999999999999996, 1.1102230246251575e-16], [-6.12323399573677e-17, 2.0, 1.0], [0.0, 1.0, 1.0000000000000002]]}, "face_connections": {"1": ["6"], "6": ["1", "3"], "3": ["6", "4", "2"], "4": ["3", "5"], "2": ["3", "5"], "5": ["4", "2"]}, "valid": false}, "base_face": "1", "folding_steps": [["6", "1", [1, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["3", "6", [1.0, 1.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["2", "3", [1.0, 1.0, 1.0], [-1.0, 0.0, 2.220446049250313e-16], -1.5707963267948966], ["5", "2", [-2.220446049250313e-16, 0.9999999999999999, 2.220446049250313e-16], [2.220446049250313e-16, 1.1102230246251565e-16, 1.0], -1.5707963267948966], ["4", "3", [0.0, 1.0, 1.0000000000000002], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 3 downwards", "Fold face 2 downwards towards face 1", "Fold face 5 downwards towards face 1", "Fold face 4 downwards towards face 6"], "images_per_step": ["output_dir/folding_nets/random3_net21_base1_step1.png", "output_dir/folding_nets/random3_net21_base1_step2.png", "output_dir/folding_nets/random3_net21_base1_step3.png"], "id": "random3_net21_base1"} | q+steps | [
"no",
"yes"
] |
|
221_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 1 as the base:
Step 1: Fold face 3 upwards
Step 2: Fold face 4 downwards
Step 3: Fold face 5 downwards towards face 1
Step 4: Fold face 2 downwards towards face 1
Step 5: Fold face 6 inwards towards face 5
Based on the above steps, can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "1-3-2 Net", "faces": {"5": [[0.9999999999999999, 3.0, 2.220446049250313e-16], [1.0, 3.0, 1.0000000000000002], [1.0, 2.0, 1.0], [0.9999999999999999, 2.0, 0.0]], "1": [[1, 2, 0], [2, 2, 0], [2, 3, 0], [1, 3, 0]], "3": [[1.0, 2.0, 1.0], [2.0, 2.0, 1.0], [2.0, 2.0, 0.0], [1.0, 2.0, 0.0]], "4": [[1.0, 3.0, 1.0000000000000002], [2.0, 3.0, 1.0000000000000002], [2.0, 2.0, 1.0], [1.0, 2.0, 1.0]], "2": [[2.0, 3.0, 1.0000000000000002], [2.0, 3.0, 2.220446049250313e-16], [2.0, 2.0, 0.0], [2.0, 2.0, 1.0]], "6": [[1.0, 3.0, 1.0000000000000004], [1.0, 3.0, 4.440892098500626e-16], [2.0, 3.0, 2.220446049250313e-16], [2.0, 3.0, 1.0000000000000002]]}, "face_connections": {"5": ["4"], "1": ["3"], "3": ["1", "4"], "4": ["5", "3", "2"], "2": ["4", "6"], "6": ["2"]}, "valid": true}, "base_face": "1", "folding_steps": [["3", "1", [1, 2, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["4", "3", [1.0, 2.0, 1.0], [1.0, 0.0, 0.0], -1.5707963267948966], ["5", "4", [1.0, 3.0, 1.0000000000000002], [0.0, -1.0, -2.220446049250313e-16], 1.5707963267948966], ["2", "4", [2.0, 3.0, 1.0000000000000002], [0.0, -1.0, -2.220446049250313e-16], -1.5707963267948966], ["6", "2", [2.0, 3.0, 1.0000000000000002], [0.0, 0.0, -1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 3 upwards", "Fold face 4 downwards", "Fold face 5 downwards towards face 1", "Fold face 2 downwards towards face 1", "Fold face 6 inwards towards face 5"], "images_per_step": ["output_dir/folding_nets/random3_net11_base1_step1.png", "output_dir/folding_nets/random3_net11_base1_step2.png", "output_dir/folding_nets/random3_net11_base1_step3.png", "output_dir/folding_nets/random3_net11_base1_step4.png", "output_dir/folding_nets/random3_net11_base1_step5.png", "output_dir/folding_nets/random3_net11_base1_step6.png"], "id": "random3_net11_base1"} | q+steps | [
"no",
"yes"
] |
|
479_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "invalid_G", "faces": {"1": [[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0]], "3": [[1.0, 0.0, 0.0], [1.0, 0.0, 1.0], [1.0, 1.0, 1.0], [1.0, 1.0, 0.0]], "2": [[1.0, 0.0, 1.0], [0.0, 0.0, 1.0000000000000002], [0.0, 1.0, 1.0000000000000002], [1.0, 1.0, 1.0]], "5": [[0.0, 0.0, 1.0000000000000002], [-2.83276944882399e-16, 0.0, 2.220446049250313e-16], [-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [0.0, 1.0, 1.0000000000000002]], "4": [[0.0, 1.0, 0.0], [1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [0.0, 1.0, 1.0]], "6": [[-4.930380657631324e-32, 1.0, 1.0000000000000002], [-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [0.9999999999999997, 1.0, -6.123233995736767e-17], [0.9999999999999999, 1.0, 0.9999999999999999]]}, "face_connections": {"1": ["3", "4"], "3": ["1", "2"], "2": ["3", "5"], "5": ["2", "6"], "4": ["1"], "6": ["5"]}, "valid": false}, "base_face": "1", "folding_steps": [["4", "1", [1, 1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["3", "1", [1, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["2", "3", [1.0, 0.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["5", "2", [0.0, 0.0, 1.0000000000000002], [0.0, 1.0, 0.0], -1.5707963267948966], ["6", "5", [-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [2.83276944882399e-16, 0.0, 1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 4 upwards", "Fold face 3 upwards towards face 4", "Fold face 2 downwards towards face 4", "Fold face 5 downwards towards face 1", "Fold face 6 downwards towards face 1"], "images_per_step": ["output_dir/folding_nets/random1_net20_base1_step1.png", "output_dir/folding_nets/random1_net20_base1_step2.png", "output_dir/folding_nets/random1_net20_base1_step3.png", "output_dir/folding_nets/random1_net20_base1_step4.png"], "id": "random1_net20_base1"} | q_only | [
"yes",
"no"
] |
|
78_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 4 as the base:
Step 1: Fold face 5 upwards
Step 2: Fold face 1 inwards towards face 4
Step 3: Fold face 3 downwards towards face 1
Step 4: Fold face 6 downwards towards face 4
Step 5: Fold face 2 inwards towards face 1
Based on the above steps, can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "1-3-2 Net", "faces": {"1": [[0.9999999999999999, 3.0, 1.0], [1.0, 2.0, 1.0], [1.0, 2.0, 0.0], [0.9999999999999999, 3.0, 0.0]], "4": [[1, 2, 0], [2, 2, 0], [2, 3, 0], [1, 3, 0]], "5": [[1.0, 2.0, 1.0], [2.0, 2.0, 1.0], [2.0, 2.0, 0.0], [1.0, 2.0, 0.0]], "3": [[1.0, 3.0, 1.0000000000000002], [2.0, 3.0, 1.0000000000000002], [2.0, 2.0, 1.0], [1.0, 2.0, 1.0]], "6": [[2.0, 3.0, 1.0000000000000002], [2.0, 3.0, 2.220446049250313e-16], [2.0, 2.0, 0.0], [2.0, 2.0, 1.0]], "2": [[1.0, 3.0, 1.0000000000000004], [1.0, 3.0, 4.440892098500626e-16], [2.0, 3.0, 2.220446049250313e-16], [2.0, 3.0, 1.0000000000000002]]}, "face_connections": {"1": ["5"], "4": ["5"], "5": ["1", "4", "3"], "3": ["5", "6"], "6": ["3", "2"], "2": ["6"]}, "valid": true}, "base_face": "4", "folding_steps": [["5", "4", [1, 2, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["1", "5", [1.0, 2.0, 1.0], [0.0, 0.0, -1.0], 1.5707963267948966], ["3", "5", [1.0, 2.0, 1.0], [1.0, 0.0, 0.0], -1.5707963267948966], ["6", "3", [2.0, 3.0, 1.0000000000000002], [0.0, -1.0, -2.220446049250313e-16], -1.5707963267948966], ["2", "6", [2.0, 3.0, 1.0000000000000002], [0.0, 0.0, -1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 5 upwards", "Fold face 1 inwards towards face 4", "Fold face 3 downwards towards face 1", "Fold face 6 downwards towards face 4", "Fold face 2 inwards towards face 1"], "images_per_step": ["output_dir/folding_nets/random2_net10_base4_step1.png", "output_dir/folding_nets/random2_net10_base4_step2.png", "output_dir/folding_nets/random2_net10_base4_step3.png", "output_dir/folding_nets/random2_net10_base4_step4.png", "output_dir/folding_nets/random2_net10_base4_step5.png", "output_dir/folding_nets/random2_net10_base4_step6.png"], "id": "random2_net10_base4"} | q+steps | [
"yes",
"no"
] |
|
102_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 4 as the base:
Step 1: Fold face 5 upwards
Step 2: Fold face 1 upwards towards face 5
Step 3: Fold face 3 downwards towards face 5
Step 4: Fold face 2 downwards towards face 5
Step 5: Fold face 6 inwards towards face 4
Based on the above steps, can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "Big T - Variant 1", "faces": {"5": [[0.9999999999999999, 0.0, 1.0], [1.0, 0.0, 0.0], [1.0, 1.0, 0.0], [0.9999999999999999, 1.0, 1.0]], "4": [[1, 0, 0], [2, 0, 0], [2, 1, 0], [1, 1, 0]], "6": [[2.0, -6.123233995736766e-17, 1.0], [2.0, 0.9999999999999999, 1.0], [2.0, 0.9999999999999999, 1.1102230246251565e-16], [2.0, -1.232595164407831e-32, 0.0]], "1": [[1.0, -6.123233995736766e-17, 1.0], [2.0, -6.123233995736766e-17, 1.0], [2.0, 0.0, 0.0], [1.0, 0.0, 0.0]], "3": [[1.0, 0.9999999999999999, 1.0000000000000002], [2.0, 0.9999999999999999, 1.0000000000000002], [2.0, -6.123233995736766e-17, 1.0], [1.0, -6.123233995736766e-17, 1.0]], "2": [[1.0, 1.0, 2.220446049250313e-16], [2.0, 1.0, 2.220446049250313e-16], [2.0, 0.9999999999999999, 1.0000000000000002], [1.0, 0.9999999999999999, 1.0000000000000002]]}, "face_connections": {"5": ["4"], "4": ["5", "1"], "6": ["1"], "1": ["4", "6", "3"], "3": ["1", "2"], "2": ["3"]}, "valid": true}, "base_face": "4", "folding_steps": [["5", "4", [1, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["1", "4", [1, 0, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["3", "1", [1.0, -6.123233995736766e-17, 1.0], [1.0, 0.0, 0.0], -1.5707963267948966], ["2", "3", [1.0, 0.9999999999999999, 1.0000000000000002], [1.0, 0.0, 0.0], -1.5707963267948966], ["6", "1", [2.0, -6.123233995736766e-17, 1.0], [0.0, 6.123233995736766e-17, -1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 5 upwards", "Fold face 1 upwards towards face 5", "Fold face 3 downwards towards face 5", "Fold face 2 downwards towards face 5", "Fold face 6 inwards towards face 4"], "images_per_step": ["output_dir/folding_nets/random2_net4_base4_step1.png", "output_dir/folding_nets/random2_net4_base4_step2.png", "output_dir/folding_nets/random2_net4_base4_step3.png", "output_dir/folding_nets/random2_net4_base4_step4.png", "output_dir/folding_nets/random2_net4_base4_step5.png", "output_dir/folding_nets/random2_net4_base4_step6.png"], "id": "random2_net4_base4"} | q+steps | [
"no",
"yes"
] |
|
187_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 3 as the base:
Step 1: Fold face 4 upwards
Step 2: Fold face 2 upwards
Step 3: Fold face 5 downwards towards face 2
Step 4: Fold face 6 upwards towards face 2
Step 5: Fold face 1 downwards towards face 3
Based on the above steps, can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "t-shaped Net Variant 2", "faces": {"3": [[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0]], "2": [[-6.123233995736766e-17, 0.0, 1.0], [0.0, 0.0, 0.0], [0.0, 1.0, 0.0], [-6.123233995736766e-17, 1.0, 1.0]], "4": [[1.0, 0.0, 0.0], [1.0, 0.0, 1.0], [1.0, 1.0, 1.0], [1.0, 1.0, 0.0]], "5": [[1.0, 0.0, 1.0], [0.0, 0.0, 1.0000000000000002], [0.0, 1.0, 1.0000000000000002], [1.0, 1.0, 1.0]], "6": [[0.0, -6.123233995736766e-17, 1.0], [1.0, -6.123233995736766e-17, 1.0], [1.0, 0.0, 0.0], [0.0, 0.0, 0.0]], "1": [[1.0, 1.0, 1.0], [0.0, 1.0, 1.0000000000000002], [-2.220446049250313e-16, 1.0, 2.220446049250313e-16], [0.9999999999999998, 1.0, 0.0]]}, "face_connections": {"1": ["5"], "2": ["3"], "3": ["2", "4", "6"], "4": ["3", "5"], "5": ["1", "4"], "6": ["3"]}, "valid": true}, "base_face": "3", "folding_steps": [["4", "3", [1, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["2", "3", [0, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["5", "4", [1.0, 0.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["6", "3", [0, 0, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["1", "5", [0.0, 1.0, 1.0000000000000002], [1.0, 0.0, -2.220446049250313e-16], -1.5707963267948966]], "folding_step_descs": ["Fold face 4 upwards", "Fold face 2 upwards", "Fold face 5 downwards towards face 2", "Fold face 6 upwards towards face 2", "Fold face 1 downwards towards face 3"], "images_per_step": ["output_dir/folding_nets/net2_base3_step1.png", "output_dir/folding_nets/net2_base3_step2.png", "output_dir/folding_nets/net2_base3_step3.png", "output_dir/folding_nets/net2_base3_step4.png", "output_dir/folding_nets/net2_base3_step5.png", "output_dir/folding_nets/net2_base3_step6.png"], "id": "net2_base3"} | q+steps | [
"no",
"yes"
] |
|
155_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 4 as the base:
Step 1: Fold face 2 upwards
Step 2: Fold face 3 inwards towards face 4
Step 3: Fold face 5 upwards towards face 3
Step 4: Fold face 6 downwards towards face 2
Step 5: Fold face 1 inwards towards face 4
Based on the above steps, can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "Big T Net", "faces": {"1": [[0.9999999999999999, -1.0, 6.123233995736766e-17], [1.0, 0.0, 0.0], [1.0, 6.123233995736765e-17, 1.0], [0.9999999999999999, -0.9999999999999999, 1.0]], "2": [[1.0, 0.0, 0.0], [2.0, 0.0, 0.0], [2.0, 6.123233995736766e-17, 1.0], [1.0, 6.123233995736766e-17, 1.0]], "3": [[2.0, 0.0, 0.0], [2.0, -1.0, 6.123233995736766e-17], [2.0, -0.9999999999999999, 1.0], [2.0, 6.123233995736765e-17, 1.0]], "4": [[1, -1, 0], [2, -1, 0], [2, 0, 0], [1, 0, 0]], "5": [[1.0, -1.0, 1.0], [2.0, -1.0, 1.0], [2.0, -1.0, 0.0], [1.0, -1.0, 0.0]], "6": [[1.0, 0.0, 1.0000000000000002], [2.0, 0.0, 1.0000000000000002], [2.0, -1.0, 1.0], [1.0, -1.0, 1.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3", "4"], "3": ["2"], "4": ["2", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": true}, "base_face": "4", "folding_steps": [["2", "4", [2, 0, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["3", "2", [2.0, 0.0, 0.0], [0.0, 6.123233995736766e-17, 1.0], -1.5707963267948966], ["5", "4", [1, -1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["6", "5", [1.0, -1.0, 1.0], [1.0, 0.0, 0.0], -1.5707963267948966], ["1", "2", [1.0, 0.0, 0.0], [0.0, 6.123233995736766e-17, 1.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 3 inwards towards face 4", "Fold face 5 upwards towards face 3", "Fold face 6 downwards towards face 2", "Fold face 1 inwards towards face 4"], "images_per_step": ["output_dir/folding_nets/net3_base4_step1.png", "output_dir/folding_nets/net3_base4_step2.png", "output_dir/folding_nets/net3_base4_step3.png", "output_dir/folding_nets/net3_base4_step4.png", "output_dir/folding_nets/net3_base4_step5.png", "output_dir/folding_nets/net3_base4_step6.png"], "id": "net3_base4"} | q+steps | [
"yes",
"no"
] |
|
244_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "invalid_F", "faces": {"1": [[0.9999999999999999, 1.0, 1.0], [1.0, 1.0, 0.0], [1.0, 2.0, 0.0], [0.9999999999999999, 2.0, 1.0]], "6": [[1, 1, 0], [2, 1, 0], [2, 2, 0], [1, 2, 0]], "3": [[2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [2.0, 2.0, 0.0]], "4": [[2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [2.0000000000000004, 2.0, 0.0], [2.0, 1.0, 0.0]], "2": [[1.0, 0.9999999999999999, 0.0], [1.0, 0.9999999999999999, 1.0], [2.0, 1.0, 1.0], [2.0, 1.0, 0.0]], "5": [[1.0, 0.9999999999999999, 1.0], [0.9999999999999999, 2.0, 1.0], [2.0, 2.0, 1.0], [2.0, 1.0, 1.0]]}, "face_connections": {"1": ["6"], "6": ["1", "3"], "3": ["6", "4", "2"], "4": ["3", "5"], "2": ["3", "5"], "5": ["4", "2"]}, "valid": false}, "base_face": "6", "folding_steps": [["1", "6", [1, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "6", [2, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["2", "3", [2.0, 1.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["5", "2", [1.0, 0.9999999999999999, 1.0], [1.0, 1.1102230246251565e-16, 0.0], -1.5707963267948966], ["4", "3", [2.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 3 upwards", "Fold face 2 inwards towards face 1", "Fold face 5 downwards towards face 1", "Fold face 4 downwards towards face 6"], "images_per_step": ["output_dir/folding_nets/random3_net21_base6_step1.png", "output_dir/folding_nets/random3_net21_base6_step2.png", "output_dir/folding_nets/random3_net21_base6_step3.png"], "id": "random3_net21_base6"} | q_only | [
"yes",
"no"
] |
|
224_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "Linear 6-Face Row", "faces": {"1": [[0.9999999999999999, 0.0, 1.0], [1.0, 0.0, 0.0], [1.0, 1.0, 0.0], [0.9999999999999999, 1.0, 1.0]], "3": [[1, 0, 0], [2, 0, 0], [2, 1, 0], [1, 1, 0]], "6": [[2.0, 0.0, 0.0], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [2.0, 1.0, 0.0]], "4": [[2.0, 0.0, 1.0], [1.0, 0.0, 1.0], [1.0, 1.0, 1.0], [2.0, 1.0, 1.0]], "2": [[1.0, 0.0, 1.0], [0.9999999999999997, 0.0, 0.0], [0.9999999999999997, 1.0, 0.0], [1.0, 1.0, 1.0]], "5": [[0.9999999999999997, 0.0, 0.0], [1.9999999999999996, 0.0, -5.053215498074303e-16], [1.9999999999999996, 1.0, -5.053215498074303e-16], [0.9999999999999997, 1.0, 0.0]]}, "face_connections": {"1": ["3"], "3": ["1", "6"], "6": ["3", "4"], "4": ["6", "2"], "2": ["4", "5"], "5": ["2"]}, "valid": false}, "base_face": "3", "folding_steps": [["1", "3", [1, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["6", "3", [2, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "6", [2.0, 0.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["2", "4", [1.0, 0.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["5", "2", [0.9999999999999997, 0.0, 0.0], [0.0, 1.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 6 upwards", "Fold face 4 downwards towards face 1", "Fold face 2 downwards towards face 1", "Fold face 5 upwards towards face 1"], "images_per_step": ["output_dir/folding_nets/random3_net12_base3_step1.png", "output_dir/folding_nets/random3_net12_base3_step2.png", "output_dir/folding_nets/random3_net12_base3_step3.png"], "id": "random3_net12_base3"} | q_only | [
"yes",
"no"
] |
|
191_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 4 as the base:
Step 1: Fold face 6 upwards
Step 2: Fold face 5 inwards towards face 4
Step 3: Fold face 1 downwards towards face 6
Step 4: Fold face 2 downwards towards face 4
Step 5: Fold face 3 upwards towards face 4
Based on the above steps, can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "Invalid D", "faces": {"4": [[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0]], "6": [[0.0, 1.0, 0.0], [1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [0.0, 1.0, 1.0]], "5": [[1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [1.0, 0.0, 1.0], [1.0, 0.0, 0.0]], "1": [[1.0, 1.0, 1.0], [1.0, 0.0, 1.0], [0.0, 0.0, 1.0000000000000002], [0.0, 1.0, 1.0000000000000002]], "2": [[1.0, 0.0, 1.0], [0.9999999999999998, -2.83276944882399e-16, 0.0], [-2.220446049250313e-16, -2.83276944882399e-16, 2.220446049250313e-16], [0.0, 0.0, 1.0000000000000002]], "3": [[0.9999999999999998, -2.83276944882399e-16, 0.0], [0.9999999999999998, 0.9999999999999997, -1.2246467991473535e-16], [-2.220446049250313e-16, 0.9999999999999997, 9.957992501029594e-17], [-2.220446049250313e-16, -2.83276944882399e-16, 2.220446049250313e-16]]}, "face_connections": {"4": ["6"], "6": ["4", "5"], "5": ["6", "1"], "1": ["5", "2"], "2": ["1", "3"], "3": ["2"]}, "valid": false}, "base_face": "4", "folding_steps": [["6", "4", [1, 1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["5", "6", [1.0, 1.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["1", "5", [1.0, 1.0, 1.0], [0.0, -1.0, 0.0], 1.5707963267948966], ["2", "1", [1.0, 0.0, 1.0], [-1.0, 0.0, 2.220446049250313e-16], -1.5707963267948966], ["3", "2", [0.9999999999999998, -2.83276944882399e-16, 0.0], [-1.0, 0.0, 2.220446049250313e-16], -1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 5 inwards towards face 4", "Fold face 1 downwards towards face 6", "Fold face 2 downwards towards face 4", "Fold face 3 upwards towards face 4"], "images_per_step": ["output_dir/folding_nets/random2_net19_base4_step1.png", "output_dir/folding_nets/random2_net19_base4_step2.png", "output_dir/folding_nets/random2_net19_base4_step3.png", "output_dir/folding_nets/random2_net19_base4_step4.png"], "id": "random2_net19_base4"} | q+steps | [
"no",
"yes"
] |
|
448_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 1 as the base:
Step 1: Fold face 2 upwards
Step 2: Fold face 3 inwards towards face 1
Step 3: Fold face 4 inwards towards face 1
Step 4: Fold face 5 inwards towards face 2
Step 5: Fold face 6 upwards towards face 2
Based on the above steps, can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "invalid_G", "faces": {"2": [[0.0, 0.9999999999999999, 1.0], [1.0, 0.9999999999999999, 1.0], [1.0, 1.0, 0.0], [0.0, 1.0, 0.0]], "3": [[1.0, 0.9999999999999999, 1.0], [1.0, 2.0, 1.0], [1.0, 2.0, 1.1102230246251565e-16], [1.0, 1.0, 0.0]], "4": [[1.0, 2.0, 1.0], [0.0, 2.0000000000000004, 1.0000000000000002], [0.0, 2.0000000000000004, 2.220446049250313e-16], [1.0, 2.0, 1.1102230246251565e-16]], "5": [[0.0, 2.0000000000000004, 1.0000000000000002], [-6.123233995736766e-17, 1.0000000000000004, 1.0000000000000004], [-6.123233995736766e-17, 1.0000000000000004, 3.3306690738754696e-16], [0.0, 2.0000000000000004, 2.220446049250313e-16]], "1": [[0, 1, 0], [1, 1, 0], [1, 2, 0], [0, 2, 0]], "6": [[-1.232595164407831e-32, 2.0000000000000004, 2.220446049250313e-16], [-6.123233995736766e-17, 1.0000000000000004, 3.3306690738754696e-16], [0.9999999999999998, 1.0000000000000004, 2.718345674301793e-16], [0.9999999999999999, 2.0000000000000004, 1.6081226496766364e-16]]}, "face_connections": {"2": ["3", "1"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4", "6"], "1": ["2"], "6": ["5"]}, "valid": false}, "base_face": "1", "folding_steps": [["2", "1", [0, 1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["3", "2", [1.0, 0.9999999999999999, 1.0], [0.0, 1.1102230246251565e-16, -1.0], -1.5707963267948966], ["4", "3", [1.0, 2.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["5", "4", [0.0, 2.0000000000000004, 1.0000000000000002], [0.0, 0.0, -1.0], -1.5707963267948966], ["6", "5", [-6.123233995736766e-17, 1.0000000000000004, 3.3306690738754696e-16], [6.123233995736766e-17, 1.0, -1.1102230246251565e-16], -1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 3 inwards towards face 1", "Fold face 4 inwards towards face 1", "Fold face 5 inwards towards face 2", "Fold face 6 upwards towards face 2"], "images_per_step": ["output_dir/folding_nets/net20_base1_step1.png", "output_dir/folding_nets/net20_base1_step2.png", "output_dir/folding_nets/net20_base1_step3.png", "output_dir/folding_nets/net20_base1_step4.png"], "id": "net20_base1"} | q+steps | [
"no",
"yes"
] |
|
298_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=2)", "faces": {"3": [[3.0, -2.83276944882399e-16, 0.0], [2.0, 0.0, 0.0], [2.0, 0.0, 1.0], [3.0, -2.83276944882399e-16, 1.0]], "5": [[2.0, 0.0, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [2.0, 0.0, 1.0]], "2": [[2.0, 1.0, 0.0], [3.0, 1.0, 0.0], [3.0, 1.0, 1.0], [2.0, 1.0, 1.0]], "6": [[3.0, 1.0, 0.0], [3.0, 0.0, 0.0], [3.0, 0.0, 1.0], [3.0, 1.0, 1.0]], "1": [[3.0, 0.0, 0.0], [2.0, -6.123233995736766e-17, 0.0], [2.0, -6.123233995736766e-17, 1.0], [3.0, 0.0, 1.0]], "4": [[2, 0, 0], [3, 0, 0], [3, 1, 0], [2, 1, 0]]}, "face_connections": {"3": ["5"], "5": ["3", "2"], "2": ["5", "6", "4"], "6": ["2", "1"], "1": ["6"], "4": ["2"]}, "valid": false}, "base_face": "4", "folding_steps": [["2", "4", [3, 1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["5", "2", [2.0, 1.0, 0.0], [0.0, 0.0, 1.0], 1.5707963267948966], ["3", "5", [2.0, 0.0, 0.0], [0.0, 0.0, 1.0], 1.5707963267948966], ["6", "2", [3.0, 1.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["1", "6", [3.0, 0.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 5 inwards towards face 4", "Fold face 3 inwards towards face 4", "Fold face 6 inwards towards face 3", "Fold face 1 inwards towards face 3"], "images_per_step": ["output_dir/folding_nets/random3_net15_base4_step1.png", "output_dir/folding_nets/random3_net15_base4_step2.png", "output_dir/folding_nets/random3_net15_base4_step3.png", "output_dir/folding_nets/random3_net15_base4_step4.png"], "id": "random3_net15_base4"} | q_only | [
"no",
"yes"
] |
|
395_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 1 as the base:
Step 1: Fold face 2 upwards
Step 2: Fold face 3 upwards towards face 2
Step 3: Fold face 5 downwards towards face 2
Step 4: Fold face 6 downwards towards face 1
Step 5: Fold face 4 inwards towards face 5
Based on the above steps, can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "invalid_G", "faces": {"6": [[4.0, 0.0, 0.0], [4.0, 0.0, 1.0], [4.0, 1.0, 1.0], [4.0, 1.0, 0.0]], "5": [[4.0, 0.0, 1.0], [3.0, 0.0, 1.0], [3.0, 1.0, 1.0], [4.0, 1.0, 1.0]], "3": [[3.0, 0.0, 1.0], [3.0, 0.0, 0.0], [3.0, 1.0, 0.0], [3.0, 1.0, 1.0]], "1": [[3, 0, 0], [4, 0, 0], [4, 1, 0], [3, 1, 0]], "4": [[4.0, 1.0, 0.0], [4.0, 1.0, 1.0], [3.0, 1.0, 1.0], [3.0, 1.0, 0.0]], "2": [[3.0, 1.0, 0.0], [4.0, 1.0, 0.0], [4.0, 1.0, 1.0], [3.0, 1.0, 1.0]]}, "face_connections": {"6": ["5", "4"], "5": ["6", "3"], "3": ["5", "1"], "1": ["3", "2"], "4": ["6"], "2": ["1"]}, "valid": false}, "base_face": "1", "folding_steps": [["2", "1", [4, 1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["3", "1", [3, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["5", "3", [3.0, 0.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["6", "5", [4.0, 0.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["4", "6", [4.0, 1.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 3 upwards towards face 2", "Fold face 5 downwards towards face 2", "Fold face 6 downwards towards face 1", "Fold face 4 inwards towards face 5"], "images_per_step": ["output_dir/folding_nets/random3_net20_base1_step1.png", "output_dir/folding_nets/random3_net20_base1_step2.png", "output_dir/folding_nets/random3_net20_base1_step3.png", "output_dir/folding_nets/random3_net20_base1_step4.png"], "id": "random3_net20_base1"} | q+steps | [
"yes",
"no"
] |
|
389_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "3-3 Net", "faces": {"1": [[2.0, 1.0, 1.0], [2.0, 1.0, 1.1102230246251565e-16], [2.0000000000000004, 0.0, 2.220446049250313e-16], [2.0000000000000004, 0.0, 1.0]], "6": [[0.9999999999999999, 1.0, 1.0], [1.0, 1.0, 0.0], [2.0, 1.0, 1.1102230246251565e-16], [2.0, 1.0, 1.0]], "5": [[0.9999999999999999, 0.0, 1.0], [1.0, 0.0, 0.0], [1.0, 1.0, 0.0], [0.9999999999999999, 1.0, 1.0]], "2": [[1, 0, 0], [2, 0, 0], [2, 1, 0], [1, 1, 0]], "4": [[1.0, -6.123233995736766e-17, 1.0], [2.0, -6.123233995736766e-17, 1.0], [2.0, 0.0, 0.0], [1.0, 0.0, 0.0]], "3": [[1.0, 0.9999999999999999, 1.0000000000000002], [2.0, 0.9999999999999999, 1.0000000000000002], [2.0, -6.123233995736766e-17, 1.0], [1.0, -6.123233995736766e-17, 1.0]]}, "face_connections": {"1": ["6"], "6": ["1", "5"], "5": ["6", "2"], "2": ["5", "4"], "4": ["2", "3"], "3": ["4"]}, "valid": true}, "base_face": "2", "folding_steps": [["5", "2", [1, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["4", "2", [1, 0, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["3", "4", [1.0, -6.123233995736766e-17, 1.0], [1.0, 0.0, 0.0], -1.5707963267948966], ["6", "5", [1.0, 1.0, 0.0], [-1.1102230246251565e-16, 0.0, 1.0], -1.5707963267948966], ["1", "6", [2.0, 1.0, 1.1102230246251565e-16], [0.0, 0.0, 1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 5 upwards", "Fold face 4 upwards towards face 5", "Fold face 3 downwards towards face 5", "Fold face 6 inwards towards face 2", "Fold face 1 downwards towards face 2"], "images_per_step": ["output_dir/folding_nets/random2_net7_base2_step1.png", "output_dir/folding_nets/random2_net7_base2_step2.png", "output_dir/folding_nets/random2_net7_base2_step3.png", "output_dir/folding_nets/random2_net7_base2_step4.png", "output_dir/folding_nets/random2_net7_base2_step5.png", "output_dir/folding_nets/random2_net7_base2_step6.png"], "id": "random2_net7_base2"} | q_only | [
"no",
"yes"
] |
|
235_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "Linear 6-Face Row", "faces": {"3": [[4.0, 0.0, 0.0], [4.0, 0.0, 1.0], [4.0, 1.0, 1.0], [4.0, 1.0, 0.0]], "2": [[4.0, 0.0, 1.0], [3.0, 0.0, 1.0], [3.0, 1.0, 1.0], [4.0, 1.0, 1.0]], "5": [[3.0, 0.0, 1.0], [3.0, 0.0, 0.0], [3.0, 1.0, 0.0], [3.0, 1.0, 1.0]], "1": [[3, 0, 0], [4, 0, 0], [4, 1, 0], [3, 1, 0]], "4": [[4.0, 0.0, 0.0], [4.0, 0.0, 1.0], [4.0, 1.0, 1.0], [4.0, 1.0, 0.0]], "6": [[4.0, 0.0, 1.0], [3.0, 0.0, 1.0], [3.0, 1.0, 1.0], [4.0, 1.0, 1.0]]}, "face_connections": {"3": ["2"], "2": ["3", "5"], "5": ["2", "1"], "1": ["5", "4"], "4": ["1", "6"], "6": ["4"]}, "valid": false}, "base_face": "1", "folding_steps": [["5", "1", [3, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "5", [3.0, 0.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["4", "1", [4, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["3", "2", [4.0, 0.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["6", "4", [4.0, 0.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 5 upwards", "Fold face 2 downwards", "Fold face 4 upwards towards face 3", "Fold face 3 downwards towards face 1", "Fold face 6 downwards towards face 3"], "images_per_step": ["output_dir/folding_nets/random1_net12_base1_step1.png", "output_dir/folding_nets/random1_net12_base1_step2.png", "output_dir/folding_nets/random1_net12_base1_step3.png"], "id": "random1_net12_base1"} | q_only | [
"no",
"yes"
] |
|
188_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "3-3 Net", "faces": {"5": [[0.0, 1.0, 1.0], [1.0, 1.0, 1.0], [1.0, 0.0, 1.0000000000000002], [0.0, 0.0, 1.0000000000000002]], "2": [[0.0, 1.0, 0.0], [1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [0.0, 1.0, 1.0]], "3": [[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0]], "6": [[1.0, 0.0, 0.0], [1.0, 0.0, 1.0], [1.0, 1.0, 1.0], [1.0, 1.0, 0.0]], "4": [[0.0, -6.123233995736766e-17, 0.0], [0.0, -6.123233995736766e-17, 1.0], [1.0, 0.0, 1.0], [1.0, 0.0, 0.0]], "1": [[-1.2246467991473532e-16, 0.9999999999999999, 0.0], [-1.2246467991473532e-16, 0.9999999999999999, 1.0], [0.0, -6.123233995736766e-17, 1.0], [0.0, -6.123233995736766e-17, 0.0]]}, "face_connections": {"5": ["2"], "2": ["5", "3"], "3": ["2", "6"], "6": ["3", "4"], "4": ["6", "1"], "1": ["4"]}, "valid": true}, "base_face": "3", "folding_steps": [["2", "3", [1, 1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["5", "2", [1.0, 1.0, 1.0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["6", "3", [1, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "6", [1.0, 0.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["1", "4", [0.0, -6.123233995736766e-17, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 5 downwards", "Fold face 6 upwards towards face 5", "Fold face 4 inwards towards face 5", "Fold face 1 inwards towards face 5"], "images_per_step": ["output_dir/folding_nets/random3_net7_base3_step1.png", "output_dir/folding_nets/random3_net7_base3_step2.png", "output_dir/folding_nets/random3_net7_base3_step3.png", "output_dir/folding_nets/random3_net7_base3_step4.png", "output_dir/folding_nets/random3_net7_base3_step5.png", "output_dir/folding_nets/random3_net7_base3_step6.png"], "id": "random3_net7_base3"} | q_only | [
"no",
"yes"
] |
|
396_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "Linear 6-Face Row", "faces": {"3": [[0.9999999999999999, 0.0, 1.0], [1.0, 0.0, 0.0], [1.0, 1.0, 0.0], [0.9999999999999999, 1.0, 1.0]], "2": [[1, 0, 0], [2, 0, 0], [2, 1, 0], [1, 1, 0]], "5": [[2.0, 0.0, 0.0], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [2.0, 1.0, 0.0]], "1": [[2.0, 0.0, 1.0], [1.0, 0.0, 1.0], [1.0, 1.0, 1.0], [2.0, 1.0, 1.0]], "4": [[1.0, 0.0, 1.0], [0.9999999999999997, 0.0, 0.0], [0.9999999999999997, 1.0, 0.0], [1.0, 1.0, 1.0]], "6": [[0.9999999999999997, 0.0, 0.0], [1.9999999999999996, 0.0, -5.053215498074303e-16], [1.9999999999999996, 1.0, -5.053215498074303e-16], [0.9999999999999997, 1.0, 0.0]]}, "face_connections": {"3": ["2"], "2": ["3", "5"], "5": ["2", "1"], "1": ["5", "4"], "4": ["1", "6"], "6": ["4"]}, "valid": false}, "base_face": "2", "folding_steps": [["5", "2", [2, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["1", "5", [2.0, 0.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "1", [1.0, 0.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["3", "2", [1, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["6", "4", [0.9999999999999997, 0.0, 0.0], [0.0, 1.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 5 upwards", "Fold face 1 downwards", "Fold face 4 downwards towards face 3", "Fold face 3 upwards towards face 1", "Fold face 6 upwards towards face 3"], "images_per_step": ["output_dir/folding_nets/random1_net12_base2_step1.png", "output_dir/folding_nets/random1_net12_base2_step2.png", "output_dir/folding_nets/random1_net12_base2_step3.png"], "id": "random1_net12_base2"} | q_only | [
"yes",
"no"
] |
|
340_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 1 as the base:
Step 1: Fold face 5 upwards
Step 2: Fold face 4 upwards towards face 5
Step 3: Fold face 2 downwards towards face 5
Step 4: Fold face 3 upwards towards face 2
Step 5: Fold face 6 downwards towards face 2
Based on the above steps, can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=2)", "faces": {"2": [[3.0, 1.0, 1.0000000000000002], [2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [3.0, 2.0, 1.0000000000000002]], "4": [[2.0, 1.0, 1.0], [2.0, 1.0, 0.0], [2.0, 2.0, 0.0], [2.0, 2.0, 1.0]], "1": [[2, 1, 0], [3, 1, 0], [3, 2, 0], [2, 2, 0]], "3": [[3.0, 1.0, 0.0], [3.0, 1.0, 1.0], [3.0, 2.0, 1.0], [3.0, 2.0, 0.0]], "6": [[3.0, 1.0, 1.0], [2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [3.0, 2.0, 1.0]], "5": [[2.0, 0.9999999999999999, 1.0], [3.0, 0.9999999999999999, 1.0], [3.0, 1.0, 0.0], [2.0, 1.0, 0.0]]}, "face_connections": {"2": ["4"], "4": ["2", "1"], "1": ["4", "3", "5"], "3": ["1", "6"], "6": ["3"], "5": ["1"]}, "valid": false}, "base_face": "1", "folding_steps": [["5", "1", [2, 1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["4", "1", [2, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "4", [2.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "1", [3, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["6", "3", [3.0, 1.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 5 upwards", "Fold face 4 upwards towards face 5", "Fold face 2 downwards towards face 5", "Fold face 3 upwards towards face 2", "Fold face 6 downwards towards face 2"], "images_per_step": ["output_dir/folding_nets/random1_net15_base1_step1.png", "output_dir/folding_nets/random1_net15_base1_step2.png", "output_dir/folding_nets/random1_net15_base1_step3.png", "output_dir/folding_nets/random1_net15_base1_step4.png"], "id": "random1_net15_base1"} | q+steps | [
"yes",
"no"
] |
|
184_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=1)", "faces": {"5": [[4.0, 1.0, 0.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [4.0, 2.0, 0.0]], "6": [[4.0, 1.0, 1.0], [3.0, 1.0, 1.0], [3.0, 2.0, 1.0], [4.0, 2.0, 1.0]], "2": [[3.0, 1.0, 1.0], [3.0, 1.0, 0.0], [3.0, 2.0, 0.0], [3.0, 2.0, 1.0]], "4": [[3, 1, 0], [4, 1, 0], [4, 2, 0], [3, 2, 0]], "1": [[4.0, 1.0, 0.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [4.0, 2.0, 0.0]], "3": [[4.0, 0.9999999999999999, 0.0], [3.0, 0.9999999999999999, 0.0], [3.0, 1.0, 1.0], [4.0, 1.0, 1.0]]}, "face_connections": {"5": ["6"], "6": ["5", "2", "3"], "2": ["6", "4"], "4": ["2", "1"], "1": ["4"], "3": ["6"]}, "valid": false}, "base_face": "4", "folding_steps": [["1", "4", [4, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["2", "4", [3, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["6", "2", [3.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["5", "6", [4.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "6", [4.0, 1.0, 1.0], [-1.0, 0.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 2 upwards", "Fold face 6 downwards towards face 1", "Fold face 5 downwards towards face 4", "Fold face 3 downwards towards face 5"], "images_per_step": ["output_dir/folding_nets/random2_net14_base4_step1.png", "output_dir/folding_nets/random2_net14_base4_step2.png", "output_dir/folding_nets/random2_net14_base4_step3.png"], "id": "random2_net14_base4"} | q_only | [
"no",
"yes"
] |
|
255_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 5 as the base:
Step 1: Fold face 6 upwards
Step 2: Fold face 4 upwards towards face 6
Step 3: Fold face 3 inwards towards face 5
Step 4: Fold face 2 inwards towards face 5
Step 5: Fold face 1 downwards towards face 3
Based on the above steps, can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "1-3-2 Net", "faces": {"1": [[2.0, 0.9999999999999996, 1.0], [3.0, 1.0, 1.0], [3.0000000000000004, 0.0, 1.0], [2.0000000000000004, -4.440892098500626e-16, 1.0]], "2": [[3.0, 1.0, 1.0], [3.0, 1.0, 0.0], [3.0000000000000004, 0.0, 0.0], [3.0000000000000004, 0.0, 1.0]], "3": [[2.0, 1.0, 1.0], [2.0, 1.0, 0.0], [3.0, 1.0, 0.0], [3.0, 1.0, 1.0]], "4": [[2.0, 0.0, 1.0], [2.0, 0.0, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, 1.0]], "5": [[2, 0, 0], [3, 0, 0], [3, 1, 0], [2, 1, 0]], "6": [[2.0, -6.123233995736766e-17, 1.0], [3.0, -6.123233995736766e-17, 1.0], [3.0, 0.0, 0.0], [2.0, 0.0, 0.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": true}, "base_face": "5", "folding_steps": [["6", "5", [2, 0, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["4", "5", [2, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "4", [2.0, 1.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["2", "3", [3.0, 1.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["1", "2", [3.0, 1.0, 1.0], [4.440892098500626e-16, -1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 4 upwards towards face 6", "Fold face 3 inwards towards face 5", "Fold face 2 inwards towards face 5", "Fold face 1 downwards towards face 3"], "images_per_step": ["output_dir/folding_nets/net9_base5_step1.png", "output_dir/folding_nets/net9_base5_step2.png", "output_dir/folding_nets/net9_base5_step3.png", "output_dir/folding_nets/net9_base5_step4.png", "output_dir/folding_nets/net9_base5_step5.png", "output_dir/folding_nets/net9_base5_step6.png"], "id": "net9_base5"} | q+steps | [
"no",
"yes"
] |
|
398_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 6 as the base:
Step 1: Fold face 2 upwards
Step 2: Fold face 5 downwards
Step 3: Fold face 1 downwards towards face 3
Step 4: Fold face 4 downwards towards face 6
Step 5: Fold face 3 upwards towards face 5
Based on the above steps, can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=4)", "faces": {"3": [[0.9999999999999999, 1.0, 1.0], [1.0, 1.0, 0.0], [1.0, 2.0, 0.0], [0.9999999999999999, 2.0, 1.0]], "6": [[1, 1, 0], [2, 1, 0], [2, 2, 0], [1, 2, 0]], "2": [[2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [2.0, 2.0, 0.0]], "5": [[2.0, 1.0, 1.0], [1.0, 1.0, 1.0], [1.0, 2.0, 1.0], [2.0, 2.0, 1.0]], "1": [[1.0, 1.0, 1.0], [0.9999999999999997, 1.0, 0.0], [0.9999999999999997, 2.0, 0.0], [1.0, 2.0, 1.0]], "4": [[2.0, 0.9999999999999999, 0.9999999999999997], [1.9999999999999996, 0.9999999999999999, -4.440892098500626e-16], [0.9999999999999997, 1.0, 0.0], [1.0, 1.0, 1.0]]}, "face_connections": {"3": ["6"], "6": ["3", "2"], "2": ["6", "5"], "5": ["2", "1"], "1": ["5", "4"], "4": ["1"]}, "valid": false}, "base_face": "6", "folding_steps": [["2", "6", [2, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["5", "2", [2.0, 1.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["1", "5", [1.0, 1.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "1", [1.0, 1.0, 1.0], [-3.3306690738754696e-16, 0.0, -1.0], -1.5707963267948966], ["3", "6", [1, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 5 downwards", "Fold face 1 downwards towards face 3", "Fold face 4 downwards towards face 6", "Fold face 3 upwards towards face 5"], "images_per_step": ["output_dir/folding_nets/random3_net17_base6_step1.png", "output_dir/folding_nets/random3_net17_base6_step2.png", "output_dir/folding_nets/random3_net17_base6_step3.png"], "id": "random3_net17_base6"} | q+steps | [
"no",
"yes"
] |
|
75_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 2 as the base:
Step 1: Fold face 5 upwards
Step 2: Fold face 4 downwards
Step 3: Fold face 1 downwards towards face 2
Step 4: Fold face 3 upwards towards face 1
Step 5: Fold face 6 inwards towards face 2
Based on the above steps, can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "Big T - Variant 3", "faces": {"6": [[0.9999999999999999, -1.0, 6.123233995736766e-17], [1.0, 0.0, 0.0], [1.0, 6.123233995736765e-17, 1.0], [0.9999999999999999, -0.9999999999999999, 1.0]], "3": [[1.0, 0.0, 0.0], [2.0, 0.0, 0.0], [2.0, 6.123233995736766e-17, 1.0], [1.0, 6.123233995736766e-17, 1.0]], "1": [[2.0, 0.0, 1.0000000000000002], [2.0, 2.220446049250313e-16, 2.220446049250313e-16], [2.0, -0.9999999999999998, 0.0], [2.0, -1.0, 1.0]], "2": [[1, -1, 0], [2, -1, 0], [2, 0, 0], [1, 0, 0]], "5": [[1.0, -1.0, 1.0], [2.0, -1.0, 1.0], [2.0, -1.0, 0.0], [1.0, -1.0, 0.0]], "4": [[1.0, 0.0, 1.0000000000000002], [2.0, 0.0, 1.0000000000000002], [2.0, -1.0, 1.0], [1.0, -1.0, 1.0]]}, "face_connections": {"6": ["3"], "3": ["6", "2"], "1": ["4"], "2": ["3", "5"], "5": ["2", "4"], "4": ["5", "1"]}, "valid": true}, "base_face": "2", "folding_steps": [["5", "2", [1, -1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["4", "5", [1.0, -1.0, 1.0], [1.0, 0.0, 0.0], -1.5707963267948966], ["1", "4", [2.0, 0.0, 1.0000000000000002], [0.0, -1.0, -2.220446049250313e-16], -1.5707963267948966], ["3", "2", [2, 0, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["6", "3", [1.0, 0.0, 0.0], [0.0, 6.123233995736766e-17, 1.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 5 upwards", "Fold face 4 downwards", "Fold face 1 downwards towards face 2", "Fold face 3 upwards towards face 1", "Fold face 6 inwards towards face 2"], "images_per_step": ["output_dir/folding_nets/random3_net6_base2_step1.png", "output_dir/folding_nets/random3_net6_base2_step2.png", "output_dir/folding_nets/random3_net6_base2_step3.png", "output_dir/folding_nets/random3_net6_base2_step4.png", "output_dir/folding_nets/random3_net6_base2_step5.png", "output_dir/folding_nets/random3_net6_base2_step6.png"], "id": "random3_net6_base2"} | q+steps | [
"yes",
"no"
] |
|
506_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "2 Rows of 3", "faces": {"2": [[0.9999999999999999, 1.0, 1.0], [1.0, 1.0, 0.0], [2.0, 1.0, 1.1102230246251565e-16], [2.0, 1.0, 1.0]], "6": [[1.0, 1.0, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [1.0, 1.0, 1.0]], "4": [[2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [1.0, 1.0, 1.0], [1.0, 1.0, 0.0]], "3": [[0.9999999999999999, 0.0, 1.0], [1.0, 0.0, 0.0], [1.0, 1.0, 0.0], [0.9999999999999999, 1.0, 1.0]], "1": [[1, 0, 0], [2, 0, 0], [2, 1, 0], [1, 1, 0]], "5": [[2.0, 0.0, 0.0], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [2.0, 1.0, 0.0]]}, "face_connections": {"2": ["6", "3"], "6": ["2", "4", "1"], "4": ["6", "5"], "3": ["2", "1"], "1": ["6", "3", "5"], "5": ["4", "1"]}, "valid": false}, "base_face": "1", "folding_steps": [["5", "1", [2, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "5", [2.0, 1.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["3", "1", [1, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "3", [1.0, 1.0, 0.0], [-1.1102230246251565e-16, 0.0, 1.0], -1.5707963267948966], ["6", "4", [2.0, 1.0, 0.0], [-1.0, 0.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 5 upwards", "Fold face 4 inwards towards face 1", "Fold face 3 upwards towards face 4", "Fold face 2 inwards towards face 4", "Fold face 6 upwards towards face 3"], "images_per_step": ["output_dir/folding_nets/random3_net18_base1_step1.png", "output_dir/folding_nets/random3_net18_base1_step2.png"], "id": "random3_net18_base1"} | q_only | [
"no",
"yes"
] |
|
57_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "3-3 Net", "faces": {"2": [[0.0, 1.0, 1.0], [1.0, 1.0, 1.0], [1.0, 0.0, 1.0000000000000002], [0.0, 0.0, 1.0000000000000002]], "4": [[0.0, 1.0, 0.0], [1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [0.0, 1.0, 1.0]], "3": [[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0]], "1": [[1.0, 0.0, 0.0], [1.0, 0.0, 1.0], [1.0, 1.0, 1.0], [1.0, 1.0, 0.0]], "6": [[0.0, -6.123233995736766e-17, 0.0], [0.0, -6.123233995736766e-17, 1.0], [1.0, 0.0, 1.0], [1.0, 0.0, 0.0]], "5": [[-1.2246467991473532e-16, 0.9999999999999999, 0.0], [-1.2246467991473532e-16, 0.9999999999999999, 1.0], [0.0, -6.123233995736766e-17, 1.0], [0.0, -6.123233995736766e-17, 0.0]]}, "face_connections": {"2": ["4"], "4": ["2", "3"], "3": ["4", "1"], "1": ["3", "6"], "6": ["1", "5"], "5": ["6"]}, "valid": true}, "base_face": "3", "folding_steps": [["1", "3", [1, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "3", [1, 1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["2", "4", [1.0, 1.0, 1.0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["6", "1", [1.0, 0.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["5", "6", [0.0, -6.123233995736766e-17, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 4 upwards towards face 1", "Fold face 2 downwards towards face 1", "Fold face 6 inwards towards face 2", "Fold face 5 inwards towards face 2"], "images_per_step": ["output_dir/folding_nets/random1_net7_base3_step1.png", "output_dir/folding_nets/random1_net7_base3_step2.png", "output_dir/folding_nets/random1_net7_base3_step3.png", "output_dir/folding_nets/random1_net7_base3_step4.png", "output_dir/folding_nets/random1_net7_base3_step5.png", "output_dir/folding_nets/random1_net7_base3_step6.png"], "id": "random1_net7_base3"} | q_only | [
"yes",
"no"
] |
|
442_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 5 as the base:
Step 1: Fold face 6 upwards
Step 2: Fold face 3 inwards towards face 5
Step 3: Fold face 2 upwards towards face 6
Step 4: Fold face 4 upwards towards face 2
Step 5: Fold face 1 inwards towards face 3
Based on the above steps, can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "2 Rows of 3", "faces": {"1": [[0.9999999999999999, 1.0, 1.0], [1.0, 1.0, 0.0], [1.0, 0.0, -4.978996250514798e-17], [1.0, 0.0, 0.9999999999999999]], "2": [[1.0, 1.0, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [1.0, 1.0, 1.0]], "3": [[2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [1.0, 1.0, 1.0], [1.0, 1.0, 0.0]], "4": [[0.9999999999999999, 0.0, 1.0], [1.0, 0.0, 0.0], [1.0, 1.0, 0.0], [0.9999999999999999, 1.0, 1.0]], "5": [[1, 0, 0], [2, 0, 0], [2, 1, 0], [1, 1, 0]], "6": [[2.0, 0.0, 0.0], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [2.0, 1.0, 0.0]]}, "face_connections": {"1": ["2", "4"], "2": ["1", "3", "5"], "3": ["2", "6"], "4": ["1", "5"], "5": ["2", "4", "6"], "6": ["3", "5"]}, "valid": false}, "base_face": "5", "folding_steps": [["6", "5", [2, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["3", "6", [2.0, 1.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["2", "3", [2.0, 1.0, 0.0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["4", "5", [1, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["1", "4", [1.0, 1.0, 0.0], [-1.1102230246251565e-16, 0.0, 1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 3 inwards towards face 5", "Fold face 2 upwards towards face 6", "Fold face 4 upwards towards face 2", "Fold face 1 inwards towards face 3"], "images_per_step": ["output_dir/folding_nets/net18_base5_step1.png", "output_dir/folding_nets/net18_base5_step2.png", "output_dir/folding_nets/net18_base5_step3.png"], "id": "net18_base5"} | q+steps | [
"no",
"yes"
] |
|
429_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "Big T Net", "faces": {"1": [[0.9999999999999999, -2.0, 0.9999999999999998], [1.0, -3.0, 1.0000000000000002], [1.0, -3.0000000000000004, 2.220446049250313e-16], [0.9999999999999999, -2.0000000000000004, -2.220446049250313e-16]], "2": [[1.0, -3.0, 1.0000000000000002], [2.0, -3.0, 1.0000000000000002], [2.0, -3.0000000000000004, 2.220446049250313e-16], [1.0, -3.0000000000000004, 2.220446049250313e-16]], "3": [[2.0, -3.0, 1.0000000000000002], [2.0, -2.0, 0.9999999999999998], [2.0, -2.0000000000000004, -2.220446049250313e-16], [2.0, -3.0000000000000004, 2.220446049250313e-16]], "4": [[1.0, -2.0, 1.0], [2.0, -2.0, 1.0], [2.0, -3.0, 1.0000000000000002], [1.0, -3.0, 1.0000000000000002]], "5": [[1.0, -2.0, 0.0], [2.0, -2.0, 0.0], [2.0, -2.0, 1.0], [1.0, -2.0, 1.0]], "6": [[1, -3, 0], [2, -3, 0], [2, -2, 0], [1, -2, 0]]}, "face_connections": {"1": ["2"], "2": ["1", "3", "4"], "3": ["2"], "4": ["2", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": true}, "base_face": "6", "folding_steps": [["5", "6", [2, -2, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["4", "5", [2.0, -2.0, 1.0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["2", "4", [2.0, -3.0, 1.0000000000000002], [-1.0, 0.0, 0.0], -1.5707963267948966], ["3", "2", [2.0, -3.0, 1.0000000000000002], [0.0, -4.440892098500626e-16, -1.0], -1.5707963267948966], ["1", "2", [1.0, -3.0, 1.0000000000000002], [0.0, -4.440892098500626e-16, -1.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 5 upwards", "Fold face 4 downwards", "Fold face 2 downwards towards face 6", "Fold face 3 downwards towards face 4", "Fold face 1 downwards towards face 4"], "images_per_step": ["output_dir/folding_nets/net3_base6_step1.png", "output_dir/folding_nets/net3_base6_step2.png", "output_dir/folding_nets/net3_base6_step3.png", "output_dir/folding_nets/net3_base6_step4.png", "output_dir/folding_nets/net3_base6_step5.png", "output_dir/folding_nets/net3_base6_step6.png"], "id": "net3_base6"} | q_only | [
"yes",
"no"
] |
|
284_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "1-3-2 Net", "faces": {"6": [[0.9999999999999999, 0.9999999999999998, 0.0], [1.0, 1.0, 1.0], [1.0, 0.0, 1.0000000000000002], [0.9999999999999999, -2.220446049250313e-16, 2.220446049250313e-16]], "2": [[1.0, 1.0, 1.0], [2.0, 1.0, 1.0], [2.0, 0.0, 1.0000000000000002], [1.0, 0.0, 1.0000000000000002]], "3": [[1.0, 1.0, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [1.0, 1.0, 1.0]], "1": [[1, 0, 0], [2, 0, 0], [2, 1, 0], [1, 1, 0]], "4": [[2.0, 0.0, 0.0], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [2.0, 1.0, 0.0]], "5": [[1.0, -6.123233995736766e-17, 0.0], [1.0, -6.123233995736766e-17, 1.0], [2.0, 0.0, 1.0], [2.0, 0.0, 0.0]]}, "face_connections": {"6": ["2"], "2": ["6", "3"], "3": ["2", "1"], "1": ["3", "4"], "4": ["1", "5"], "5": ["4"]}, "valid": true}, "base_face": "1", "folding_steps": [["4", "1", [2, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["5", "4", [2.0, 0.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["3", "1", [2, 1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["2", "3", [2.0, 1.0, 1.0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["6", "2", [1.0, 1.0, 1.0], [0.0, -1.0, 2.220446049250313e-16], 1.5707963267948966]], "folding_step_descs": ["Fold face 4 upwards", "Fold face 5 inwards towards face 1", "Fold face 3 upwards towards face 4", "Fold face 2 downwards towards face 4", "Fold face 6 downwards towards face 3"], "images_per_step": ["output_dir/folding_nets/random3_net9_base1_step1.png", "output_dir/folding_nets/random3_net9_base1_step2.png", "output_dir/folding_nets/random3_net9_base1_step3.png", "output_dir/folding_nets/random3_net9_base1_step4.png", "output_dir/folding_nets/random3_net9_base1_step5.png", "output_dir/folding_nets/random3_net9_base1_step6.png"], "id": "random3_net9_base1"} | q_only | [
"no",
"yes"
] |
|
103_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 4 as the base:
Step 1: Fold face 3 upwards
Step 2: Fold face 5 inwards towards face 4
Step 3: Fold face 6 inwards towards face 4
Step 4: Fold face 1 inwards towards face 3
Step 5: Fold face 2 inwards towards face 3
Based on the above steps, can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=0)", "faces": {"3": [[0.0, 1.0, 0.0], [1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [0.0, 1.0, 1.0]], "5": [[1.0, 1.0, 0.0], [1.0, 0.0, 0.0], [1.0, 0.0, 1.0], [1.0, 1.0, 1.0]], "6": [[1.0, 0.0, 0.0], [0.0, -2.83276944882399e-16, 0.0], [0.0, -2.83276944882399e-16, 1.0], [1.0, 0.0, 1.0]], "1": [[0.0, -2.83276944882399e-16, 0.0], [-1.2246467991473535e-16, 0.9999999999999997, 0.0], [-1.2246467991473535e-16, 0.9999999999999997, 1.0], [0.0, -2.83276944882399e-16, 1.0]], "2": [[-1.2246467991473535e-16, 0.9999999999999997, 0.0], [0.9999999999999999, 0.9999999999999999, 0.0], [0.9999999999999999, 0.9999999999999999, 1.0], [-1.2246467991473535e-16, 0.9999999999999997, 1.0]], "4": [[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0]]}, "face_connections": {"3": ["5", "4"], "5": ["3", "6"], "6": ["5", "1"], "1": ["6", "2"], "2": ["1"], "4": ["3"]}, "valid": false}, "base_face": "4", "folding_steps": [["3", "4", [1, 1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["5", "3", [1.0, 1.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["6", "5", [1.0, 0.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["1", "6", [0.0, -2.83276944882399e-16, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["2", "1", [-1.2246467991473535e-16, 0.9999999999999997, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 3 upwards", "Fold face 5 inwards towards face 4", "Fold face 6 inwards towards face 4", "Fold face 1 inwards towards face 3", "Fold face 2 inwards towards face 3"], "images_per_step": ["output_dir/folding_nets/random2_net13_base4_step1.png", "output_dir/folding_nets/random2_net13_base4_step2.png", "output_dir/folding_nets/random2_net13_base4_step3.png", "output_dir/folding_nets/random2_net13_base4_step4.png"], "id": "random2_net13_base4"} | q+steps | [
"no",
"yes"
] |
|
31_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "Invalid D", "faces": {"1": [[2.0, 0.9999999999999999, -1.0], [2.0, 0.9999999999999999, -1.1102230246251565e-16], [1.0, 1.0, 0.0], [0.9999999999999999, 1.0, -1.0]], "2": [[0.9999999999999999, 1.0, -1.0], [1.0, 1.0, 0.0], [1.0, 2.0, 0.0], [0.9999999999999999, 2.0, -1.0]], "5": [[1, 1, 0], [1, 2, 0], [2, 2, 0], [2, 1, 0]], "6": [[1.0, 2.0, 0.0], [2.0, 2.0, 0.0], [2.0, 2.0, -1.0], [1.0, 2.0, -1.0]], "3": [[2.0, 2.0, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, -1.0], [2.0, 2.0, -1.0]], "4": [[2.0, 1.0, 0.0], [1.0, 0.9999999999999999, 0.0], [1.0, 0.9999999999999999, -1.0], [2.0, 1.0, -1.0]]}, "face_connections": {"1": ["2"], "2": ["1", "5"], "5": ["2", "6"], "6": ["5", "3"], "3": ["6", "4"], "4": ["3"]}, "valid": false}, "base_face": "5", "folding_steps": [["2", "5", [1, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["1", "2", [0.9999999999999999, 1.0, -1.0], [1.1102230246251565e-16, 0.0, 1.0], 1.5707963267948966], ["6", "5", [1, 2, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["3", "6", [2.0, 2.0, 0.0], [0.0, 0.0, -1.0], 1.5707963267948966], ["4", "3", [2.0, 1.0, 0.0], [0.0, 0.0, -1.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 1 inwards towards face 5", "Fold face 6 upwards towards face 2", "Fold face 3 inwards towards face 1", "Fold face 4 inwards towards face 1"], "images_per_step": ["output_dir/folding_nets/random1_net19_base5_step1.png", "output_dir/folding_nets/random1_net19_base5_step2.png", "output_dir/folding_nets/random1_net19_base5_step3.png", "output_dir/folding_nets/random1_net19_base5_step4.png"], "id": "random1_net19_base5"} | q_only | [
"yes",
"no"
] |
|
217_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 1 as the base:
Step 1: Fold face 3 upwards
Step 2: Fold face 5 inwards towards face 1
Step 3: Fold face 4 inwards towards face 1
Step 4: Fold face 6 upwards towards face 4
Step 5: Fold face 2 downwards towards face 4
Based on the above steps, can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "Big T Net", "faces": {"4": [[0.9999999999999999, -1.0, 6.123233995736766e-17], [1.0, 0.0, 0.0], [1.0, 6.123233995736765e-17, 1.0], [0.9999999999999999, -0.9999999999999999, 1.0]], "3": [[1.0, 0.0, 0.0], [2.0, 0.0, 0.0], [2.0, 6.123233995736766e-17, 1.0], [1.0, 6.123233995736766e-17, 1.0]], "5": [[2.0, 0.0, 0.0], [2.0, -1.0, 6.123233995736766e-17], [2.0, -0.9999999999999999, 1.0], [2.0, 6.123233995736765e-17, 1.0]], "1": [[1, -1, 0], [2, -1, 0], [2, 0, 0], [1, 0, 0]], "6": [[1.0, -1.0, 1.0], [2.0, -1.0, 1.0], [2.0, -1.0, 0.0], [1.0, -1.0, 0.0]], "2": [[1.0, 0.0, 1.0000000000000002], [2.0, 0.0, 1.0000000000000002], [2.0, -1.0, 1.0], [1.0, -1.0, 1.0]]}, "face_connections": {"4": ["3"], "3": ["4", "5", "1"], "5": ["3"], "1": ["3", "6"], "6": ["1", "2"], "2": ["6"]}, "valid": true}, "base_face": "1", "folding_steps": [["3", "1", [2, 0, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["5", "3", [2.0, 0.0, 0.0], [0.0, 6.123233995736766e-17, 1.0], -1.5707963267948966], ["4", "3", [1.0, 0.0, 0.0], [0.0, 6.123233995736766e-17, 1.0], 1.5707963267948966], ["6", "1", [1, -1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["2", "6", [1.0, -1.0, 1.0], [1.0, 0.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 3 upwards", "Fold face 5 inwards towards face 1", "Fold face 4 inwards towards face 1", "Fold face 6 upwards towards face 4", "Fold face 2 downwards towards face 4"], "images_per_step": ["output_dir/folding_nets/random3_net3_base1_step1.png", "output_dir/folding_nets/random3_net3_base1_step2.png", "output_dir/folding_nets/random3_net3_base1_step3.png", "output_dir/folding_nets/random3_net3_base1_step4.png", "output_dir/folding_nets/random3_net3_base1_step5.png", "output_dir/folding_nets/random3_net3_base1_step6.png"], "id": "random3_net3_base1"} | q+steps | [
"no",
"yes"
] |
|
293_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "1-3-2 Net", "faces": {"6": [[0, 2, 0], [1, 2, 0], [1, 3, 0], [0, 3, 0]], "2": [[1.0, 2.0, 0.0], [1.0, 2.0, 1.0], [1.0, 3.0, 1.0], [1.0, 3.0, 0.0]], "3": [[0.0, 2.0, 0.0], [0.0, 2.0, 1.0], [1.0, 2.0, 1.0], [1.0, 2.0, 0.0]], "1": [[-2.83276944882399e-16, 3.0, 0.0], [-2.83276944882399e-16, 3.0, 1.0], [0.0, 2.0, 1.0], [0.0, 2.0, 0.0]], "4": [[-2.83276944882399e-16, 3.0, 1.0], [0.9999999999999997, 3.0000000000000004, 1.0000000000000002], [0.9999999999999999, 2.0000000000000004, 1.0000000000000002], [-4.930380657631324e-32, 2.0, 1.0]], "5": [[9.957992501029601e-17, 3.0, 0.0], [1.0000000000000002, 3.0000000000000004, 6.661338147750939e-16], [0.9999999999999997, 3.0000000000000004, 1.0000000000000002], [-2.83276944882399e-16, 3.0, 1.0]]}, "face_connections": {"6": ["2"], "2": ["6", "3"], "3": ["2", "1"], "1": ["3", "4"], "4": ["1", "5"], "5": ["4"]}, "valid": true}, "base_face": "6", "folding_steps": [["2", "6", [1, 2, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["3", "2", [1.0, 2.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["1", "3", [0.0, 2.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["4", "1", [-2.83276944882399e-16, 3.0, 1.0], [2.83276944882399e-16, -1.0, 0.0], -1.5707963267948966], ["5", "4", [-2.83276944882399e-16, 3.0, 1.0], [1.0, 4.440892098500626e-16, 2.220446049250313e-16], -1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 3 inwards towards face 6", "Fold face 1 inwards towards face 6", "Fold face 4 downwards towards face 2", "Fold face 5 downwards towards face 6"], "images_per_step": ["output_dir/folding_nets/random3_net9_base6_step1.png", "output_dir/folding_nets/random3_net9_base6_step2.png", "output_dir/folding_nets/random3_net9_base6_step3.png", "output_dir/folding_nets/random3_net9_base6_step4.png", "output_dir/folding_nets/random3_net9_base6_step5.png", "output_dir/folding_nets/random3_net9_base6_step6.png"], "id": "random3_net9_base6"} | q_only | [
"yes",
"no"
] |
|
319_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "t-shaped Net", "faces": {"3": [[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0]], "1": [[0.0, 1.0, 0.0], [1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [0.0, 1.0, 1.0]], "2": [[-6.123233995736766e-17, 0.0, 1.0], [0.0, 0.0, 0.0], [0.0, 1.0, 0.0], [-6.123233995736766e-17, 1.0, 1.0]], "4": [[1.0, 0.0, 0.0], [1.0, 0.0, 1.0], [1.0, 1.0, 1.0], [1.0, 1.0, 0.0]], "5": [[1.0, 0.0, 1.0], [0.0, 0.0, 1.0000000000000002], [0.0, 1.0, 1.0000000000000002], [1.0, 1.0, 1.0]], "6": [[0.0, -6.123233995736766e-17, 1.0], [1.0, -6.123233995736766e-17, 1.0], [1.0, 0.0, 0.0], [0.0, 0.0, 0.0]]}, "face_connections": {"1": ["3"], "2": ["3"], "3": ["1", "2", "4", "6"], "4": ["3", "5"], "5": ["4"], "6": ["3"]}, "valid": true}, "base_face": "3", "folding_steps": [["6", "3", [0, 0, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["2", "3", [0, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["4", "3", [1, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["5", "4", [1.0, 0.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["1", "3", [1, 1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 2 upwards towards face 6", "Fold face 4 upwards towards face 6", "Fold face 5 downwards towards face 2", "Fold face 1 upwards towards face 2"], "images_per_step": ["output_dir/folding_nets/net0_base3_step1.png", "output_dir/folding_nets/net0_base3_step2.png", "output_dir/folding_nets/net0_base3_step3.png", "output_dir/folding_nets/net0_base3_step4.png", "output_dir/folding_nets/net0_base3_step5.png", "output_dir/folding_nets/net0_base3_step6.png"], "id": "net0_base3"} | q_only | [
"no",
"yes"
] |
|
161_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "Net H: Two rows with bottom row shifted right", "faces": {"4": [[3.0, 1.0, 1.0000000000000002], [2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [3.0, 2.0, 1.0000000000000002]], "1": [[2.0, 1.0, 1.0], [2.0, 1.0, 0.0], [2.0, 2.0, 0.0], [2.0, 2.0, 1.0]], "3": [[2, 1, 0], [3, 1, 0], [3, 2, 0], [2, 2, 0]], "5": [[3.0, 0.9999999999999999, 1.0], [3.0, 0.9999999999999999, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, 1.0]], "2": [[2.0, 0.9999999999999999, 1.0], [3.0, 0.9999999999999999, 1.0], [3.0, 1.0, 0.0], [2.0, 1.0, 0.0]], "6": [[3.0, 0.9999999999999999, 1.0], [3.0, 2.0, 1.0], [3.0, 2.0, 1.1102230246251565e-16], [3.0, 1.0, 0.0]]}, "face_connections": {"4": ["1"], "1": ["4", "3", "5"], "3": ["1", "2"], "5": ["1", "2"], "2": ["3", "5", "6"], "6": ["2"]}, "valid": false}, "base_face": "3", "folding_steps": [["1", "3", [2, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["5", "1", [2.0, 1.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["2", "3", [2, 1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["4", "1", [2.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["6", "2", [3.0, 0.9999999999999999, 1.0], [0.0, 1.1102230246251565e-16, -1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 5 inwards towards face 3", "Fold face 2 upwards towards face 1", "Fold face 4 downwards towards face 5", "Fold face 6 inwards towards face 4"], "images_per_step": ["output_dir/folding_nets/random1_net23_base3_step1.png", "output_dir/folding_nets/random1_net23_base3_step2.png"], "id": "random1_net23_base3"} | q_only | [
"no",
"yes"
] |
|
565_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=0)", "faces": {"3": [[3.0, 1.0, 1.0000000000000002], [2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [3.0, 2.0, 1.0000000000000002]], "6": [[2.0, 1.0, 1.0], [2.0, 1.0, 0.0], [2.0, 2.0, 0.0], [2.0, 2.0, 1.0]], "2": [[2, 1, 0], [3, 1, 0], [3, 2, 0], [2, 2, 0]], "4": [[3.0, 1.0, 0.0], [3.0, 1.0, 1.0], [3.0, 2.0, 1.0], [3.0, 2.0, 0.0]], "5": [[3.0, 1.0, 1.0], [2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [3.0, 2.0, 1.0]], "1": [[3.0, 0.9999999999999999, 2.220446049250313e-16], [2.0, 0.9999999999999999, 0.0], [2.0, 1.0, 1.0], [3.0, 1.0, 1.0000000000000002]]}, "face_connections": {"3": ["6", "1"], "6": ["3", "2"], "2": ["6", "4"], "4": ["2", "5"], "5": ["4"], "1": ["3"]}, "valid": false}, "base_face": "2", "folding_steps": [["4", "2", [3, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["5", "4", [3.0, 1.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["6", "2", [2, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "6", [2.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["1", "3", [3.0, 1.0, 1.0000000000000002], [-1.0, 0.0, -2.220446049250313e-16], -1.5707963267948966]], "folding_step_descs": ["Fold face 4 upwards", "Fold face 5 downwards", "Fold face 6 upwards towards face 5", "Fold face 3 downwards towards face 4", "Fold face 1 downwards towards face 6"], "images_per_step": ["output_dir/folding_nets/random1_net13_base2_step1.png", "output_dir/folding_nets/random1_net13_base2_step2.png", "output_dir/folding_nets/random1_net13_base2_step3.png"], "id": "random1_net13_base2"} | q_only | [
"no",
"yes"
] |
|
534_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 4 as the base:
Step 1: Fold face 2 upwards
Step 2: Fold face 5 inwards towards face 4
Step 3: Fold face 3 upwards towards face 5
Step 4: Fold face 6 downwards towards face 2
Step 5: Fold face 1 downwards towards face 2
Based on the above steps, can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "3-3 Net", "faces": {"1": [[2.0, -0.9999999999999999, 1.0], [2.0, 1.1442377452219642e-17, 1.0], [2.0000000000000004, -3.8347585052928364e-17, 0.0], [2.0000000000000004, -0.9999999999999999, 0.0]], "6": [[0.9999999999999999, -0.9999999999999999, 1.0], [1.0, 6.123233995736765e-17, 1.0], [2.0, 1.1442377452219642e-17, 1.0], [2.0, -0.9999999999999999, 1.0]], "5": [[0.9999999999999999, -1.0, 6.123233995736766e-17], [1.0, 0.0, 0.0], [1.0, 6.123233995736765e-17, 1.0], [0.9999999999999999, -0.9999999999999999, 1.0]], "2": [[1.0, 0.0, 0.0], [2.0, 0.0, 0.0], [2.0, 6.123233995736766e-17, 1.0], [1.0, 6.123233995736766e-17, 1.0]], "4": [[1, -1, 0], [2, -1, 0], [2, 0, 0], [1, 0, 0]], "3": [[1.0, -1.0, 1.0], [2.0, -1.0, 1.0], [2.0, -1.0, 0.0], [1.0, -1.0, 0.0]]}, "face_connections": {"1": ["6"], "6": ["1", "5"], "5": ["6", "2"], "2": ["5", "4"], "4": ["2", "3"], "3": ["4"]}, "valid": true}, "base_face": "4", "folding_steps": [["2", "4", [2, 0, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["5", "2", [1.0, 0.0, 0.0], [0.0, 6.123233995736766e-17, 1.0], 1.5707963267948966], ["3", "4", [1, -1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["6", "5", [1.0, 6.123233995736765e-17, 1.0], [-1.1102230246251565e-16, -1.0, 0.0], -1.5707963267948966], ["1", "6", [2.0, 1.1442377452219642e-17, 1.0], [0.0, -1.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 5 inwards towards face 4", "Fold face 3 upwards towards face 5", "Fold face 6 downwards towards face 2", "Fold face 1 downwards towards face 2"], "images_per_step": ["output_dir/folding_nets/random2_net7_base4_step1.png", "output_dir/folding_nets/random2_net7_base4_step2.png", "output_dir/folding_nets/random2_net7_base4_step3.png", "output_dir/folding_nets/random2_net7_base4_step4.png", "output_dir/folding_nets/random2_net7_base4_step5.png", "output_dir/folding_nets/random2_net7_base4_step6.png"], "id": "random2_net7_base4"} | q+steps | [
"yes",
"no"
] |
|
129_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "Invalid D", "faces": {"1": [[0.0, 0.9999999999999999, 1.0], [1.0, 0.9999999999999999, 1.0], [1.0, 1.0, 0.0], [0.0, 1.0, 0.0]], "2": [[0, 1, 0], [1, 1, 0], [1, 2, 0], [0, 2, 0]], "3": [[1.0, 1.0, 0.0], [1.0, 2.0, 0.0], [1.0, 2.0, 1.0], [1.0, 1.0, 1.0]], "4": [[1.0, 2.0, 0.0], [1.0, 2.0, 1.0], [0.0, 2.0, 1.0], [0.0, 2.0, 0.0]], "5": [[1.0, 2.0, 1.0], [1.0, 1.0, 1.0], [0.0, 1.0, 1.0000000000000004], [0.0, 2.0, 1.0]], "6": [[1.0, 1.0, 1.0], [0.9999999999999996, 0.9999999999999997, 0.0], [-4.440892098500626e-16, 0.9999999999999997, 4.440892098500626e-16], [0.0, 1.0, 1.0000000000000004]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": false}, "base_face": "2", "folding_steps": [["1", "2", [0, 1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["3", "2", [1, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "3", [1.0, 2.0, 0.0], [0.0, 0.0, 1.0], 1.5707963267948966], ["5", "4", [1.0, 2.0, 1.0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["6", "5", [1.0, 1.0, 1.0], [-1.0, 0.0, 4.440892098500626e-16], -1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 3 upwards towards face 1", "Fold face 4 inwards towards face 2", "Fold face 5 downwards towards face 1", "Fold face 6 downwards towards face 1"], "images_per_step": ["output_dir/folding_nets/net19_base2_step1.png", "output_dir/folding_nets/net19_base2_step2.png", "output_dir/folding_nets/net19_base2_step3.png", "output_dir/folding_nets/net19_base2_step4.png"], "id": "net19_base2"} | q_only | [
"no",
"yes"
] |
|
33_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "2 Rows of 3", "faces": {"2": [[3.0, -1.0000000000000002, -0.9999999999999998], [3.0, -2.220446049250313e-16, -0.9999999999999998], [3.0, -4.440892098500626e-16, 2.220446049250313e-16], [3.0, -1.0000000000000004, 2.220446049250313e-16]], "6": [[3.0, -2.220446049250313e-16, -0.9999999999999998], [2.0, -1.6081226496766359e-16, -1.0], [2.0, -3.828568698926949e-16, 0.0], [3.0, -4.440892098500626e-16, 2.220446049250313e-16]], "4": [[2.0, 1.0, 0.0], [3.0, 1.0, 0.0], [3.0, 1.0, 1.0], [2.0, 1.0, 1.0]], "3": [[1.9999999999999998, -1.0, -0.9999999999999999], [2.0, 0.0, -0.9999999999999999], [3.0, -2.220446049250313e-16, -0.9999999999999998], [3.0, -1.0000000000000002, -0.9999999999999998]], "1": [[2.0, 0.0, 1.0], [2.0, 0.0, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, 1.0]], "5": [[2, 0, 0], [3, 0, 0], [3, 1, 0], [2, 1, 0]]}, "face_connections": {"2": ["6", "3"], "6": ["2", "4", "1"], "4": ["6", "5"], "3": ["2", "1"], "1": ["6", "3", "5"], "5": ["4", "1"]}, "valid": false}, "base_face": "5", "folding_steps": [["1", "5", [2, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["4", "5", [3, 1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["3", "1", [1.9999999999999998, -1.0, -0.9999999999999999], [2.220446049250313e-16, 1.0, 0.0], 1.5707963267948966], ["2", "3", [3.0, -2.220446049250313e-16, -0.9999999999999998], [0.0, -1.0, 0.0], 1.5707963267948966], ["6", "2", [3.0, -2.220446049250313e-16, -0.9999999999999998], [0.0, -2.220446049250313e-16, 1.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 4 upwards towards face 1", "Fold face 3 downwards", "Fold face 2 upwards", "Fold face 6 downwards towards face 3"], "images_per_step": ["output_dir/folding_nets/random3_net18_base5_step1.png", "output_dir/folding_nets/random3_net18_base5_step2.png"], "id": "random3_net18_base5"} | q_only | [
"yes",
"no"
] |
|
507_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 1 as the base:
Step 1: Fold face 3 upwards
Step 2: Fold face 2 inwards towards face 1
Step 3: Fold face 6 inwards towards face 1
Step 4: Fold face 4 inwards towards face 1
Step 5: Fold face 5 upwards towards face 1
Based on the above steps, can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "invalid_E", "faces": {"5": [[4.0, 1.0, 3.3306690738754696e-16], [4.0, 2.0, 2.220446049250313e-16], [3.0, 2.0, 1.6081226496766364e-16], [3.0, 1.0, -6.163438522699459e-16]], "1": [[3, 1, 0], [4, 1, 0], [4, 2, 0], [3, 2, 0]], "4": [[4.0, 1.0, 1.0000000000000004], [4.0, 2.0, 1.0000000000000002], [4.0, 2.0, 2.220446049250313e-16], [4.0, 1.0, 3.3306690738754696e-16]], "6": [[4.0, 2.0, 1.0000000000000002], [3.0, 2.0, 1.0], [3.0, 2.0, 1.1102230246251565e-16], [4.0, 2.0, 2.220446049250313e-16]], "2": [[3.0, 2.0, 1.0], [3.0, 0.9999999999999999, 1.0], [3.0, 1.0, 0.0], [3.0, 2.0, 1.1102230246251565e-16]], "3": [[3.0, 0.9999999999999999, 1.0], [4.0, 0.9999999999999999, 1.0], [4.0, 1.0, 0.0], [3.0, 1.0, 0.0]]}, "face_connections": {"5": ["4"], "1": ["3"], "4": ["5", "6"], "6": ["4", "2"], "2": ["6", "3"], "3": ["2", "1"]}, "valid": false}, "base_face": "1", "folding_steps": [["3", "1", [3, 1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["2", "3", [3.0, 0.9999999999999999, 1.0], [0.0, 1.1102230246251565e-16, -1.0], 1.5707963267948966], ["6", "2", [3.0, 2.0, 1.0], [0.0, 0.0, -1.0], 1.5707963267948966], ["4", "6", [4.0, 2.0, 1.0000000000000002], [0.0, 0.0, -1.0], 1.5707963267948966], ["5", "4", [4.0, 2.0, 2.220446049250313e-16], [0.0, -1.0, 1.1102230246251565e-16], -1.5707963267948966]], "folding_step_descs": ["Fold face 3 upwards", "Fold face 2 inwards towards face 1", "Fold face 6 inwards towards face 1", "Fold face 4 inwards towards face 1", "Fold face 5 upwards towards face 1"], "images_per_step": ["output_dir/folding_nets/random2_net22_base1_step1.png", "output_dir/folding_nets/random2_net22_base1_step2.png", "output_dir/folding_nets/random2_net22_base1_step3.png", "output_dir/folding_nets/random2_net22_base1_step4.png"], "id": "random2_net22_base1"} | q+steps | [
"no",
"yes"
] |
|
572_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 3 as the base:
Step 1: Fold face 1 upwards
Step 2: Fold face 2 upwards
Step 3: Fold face 5 downwards towards face 1
Step 4: Fold face 4 inwards towards face 3
Step 5: Fold face 6 downwards towards face 1
Based on the above steps, can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "invalid_G", "faces": {"1": [[0.9999999999999999, 0.0, 1.0], [1.0, 0.0, 0.0], [1.0, 1.0, 0.0], [0.9999999999999999, 1.0, 1.0]], "3": [[1, 0, 0], [2, 0, 0], [2, 1, 0], [1, 1, 0]], "2": [[2.0, 0.0, 0.0], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [2.0, 1.0, 0.0]], "5": [[2.0, 0.0, 1.0], [1.0, 0.0, 1.0], [1.0, 1.0, 1.0], [2.0, 1.0, 1.0]], "4": [[0.9999999999999999, 1.0, 1.0], [1.0, 1.0, 0.0], [2.0, 1.0, 1.1102230246251565e-16], [2.0, 1.0, 1.0]], "6": [[2.0, 1.0, 1.0], [1.0, 1.0, 1.0], [1.0, 1.0, 0.0], [2.0, 1.0, 0.0]]}, "face_connections": {"1": ["3", "4"], "3": ["1", "2"], "2": ["3", "5"], "5": ["2", "6"], "4": ["1"], "6": ["5"]}, "valid": false}, "base_face": "3", "folding_steps": [["1", "3", [1, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "3", [2, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["5", "2", [2.0, 0.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "1", [1.0, 1.0, 0.0], [-1.1102230246251565e-16, 0.0, 1.0], -1.5707963267948966], ["6", "5", [1.0, 1.0, 1.0], [1.0, 0.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 2 upwards", "Fold face 5 downwards towards face 1", "Fold face 4 inwards towards face 3", "Fold face 6 downwards towards face 1"], "images_per_step": ["output_dir/folding_nets/random1_net20_base3_step1.png", "output_dir/folding_nets/random1_net20_base3_step2.png", "output_dir/folding_nets/random1_net20_base3_step3.png", "output_dir/folding_nets/random1_net20_base3_step4.png"], "id": "random1_net20_base3"} | q+steps | [
"no",
"yes"
] |
|
72_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "1-3-2 Net", "faces": {"6": [[0.9999999999999999, 0.0, 1.0], [1.0, 0.0, 0.0], [1.0, 1.0, 0.0], [0.9999999999999999, 1.0, 1.0]], "4": [[1.0, 1.0, 1.0], [2.0, 1.0, 1.0], [2.0, 0.0, 1.0000000000000002], [1.0, 0.0, 1.0000000000000002]], "5": [[1.0, 1.0, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [1.0, 1.0, 1.0]], "1": [[1, 0, 0], [2, 0, 0], [2, 1, 0], [1, 1, 0]], "3": [[2.0, 0.0, 0.0], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [2.0, 1.0, 0.0]], "2": [[1.0, -6.123233995736766e-17, 0.0], [1.0, -6.123233995736766e-17, 1.0], [2.0, 0.0, 1.0], [2.0, 0.0, 0.0]]}, "face_connections": {"6": ["1"], "4": ["5"], "5": ["4", "1"], "1": ["6", "5", "3"], "3": ["1", "2"], "2": ["3"]}, "valid": true}, "base_face": "1", "folding_steps": [["5", "1", [2, 1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["4", "5", [2.0, 1.0, 1.0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["3", "1", [2, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["2", "3", [2.0, 0.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["6", "1", [1, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 5 upwards", "Fold face 4 downwards", "Fold face 3 upwards towards face 4", "Fold face 2 inwards towards face 4", "Fold face 6 upwards towards face 4"], "images_per_step": ["output_dir/folding_nets/random1_net11_base1_step1.png", "output_dir/folding_nets/random1_net11_base1_step2.png", "output_dir/folding_nets/random1_net11_base1_step3.png", "output_dir/folding_nets/random1_net11_base1_step4.png", "output_dir/folding_nets/random1_net11_base1_step5.png", "output_dir/folding_nets/random1_net11_base1_step6.png"], "id": "random1_net11_base1"} | q_only | [
"yes",
"no"
] |
|
399_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 4 as the base:
Step 1: Fold face 5 upwards
Step 2: Fold face 2 downwards
Step 3: Fold face 1 upwards towards face 2
Step 4: Fold face 3 downwards towards face 1
Step 5: Fold face 6 downwards towards face 2
Based on the above steps, can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "Big T - Variant 3", "faces": {"6": [[0.9999999999999999, -2.0, 0.9999999999999998], [1.0, -3.0, 1.0000000000000002], [1.0, -3.0000000000000004, 2.220446049250313e-16], [0.9999999999999999, -2.0000000000000004, -2.220446049250313e-16]], "3": [[1.0, -3.0, 1.0000000000000002], [2.0, -3.0, 1.0000000000000002], [2.0, -3.0000000000000004, 2.220446049250313e-16], [1.0, -3.0000000000000004, 2.220446049250313e-16]], "1": [[2.0, -3.0, 0.0], [2.0, -3.0, 1.0], [2.0, -2.0, 1.0], [2.0, -2.0, 0.0]], "2": [[1.0, -2.0, 1.0], [2.0, -2.0, 1.0], [2.0, -3.0, 1.0000000000000002], [1.0, -3.0, 1.0000000000000002]], "5": [[1.0, -2.0, 0.0], [2.0, -2.0, 0.0], [2.0, -2.0, 1.0], [1.0, -2.0, 1.0]], "4": [[1, -3, 0], [2, -3, 0], [2, -2, 0], [1, -2, 0]]}, "face_connections": {"6": ["3"], "3": ["6", "2"], "1": ["4"], "2": ["3", "5"], "5": ["2", "4"], "4": ["5", "1"]}, "valid": true}, "base_face": "4", "folding_steps": [["5", "4", [2, -2, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["2", "5", [2.0, -2.0, 1.0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["1", "4", [2, -3, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["3", "2", [2.0, -3.0, 1.0000000000000002], [-1.0, 0.0, 0.0], -1.5707963267948966], ["6", "3", [1.0, -3.0, 1.0000000000000002], [0.0, -4.440892098500626e-16, -1.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 5 upwards", "Fold face 2 downwards", "Fold face 1 upwards towards face 2", "Fold face 3 downwards towards face 1", "Fold face 6 downwards towards face 2"], "images_per_step": ["output_dir/folding_nets/random3_net6_base4_step1.png", "output_dir/folding_nets/random3_net6_base4_step2.png", "output_dir/folding_nets/random3_net6_base4_step3.png", "output_dir/folding_nets/random3_net6_base4_step4.png", "output_dir/folding_nets/random3_net6_base4_step5.png", "output_dir/folding_nets/random3_net6_base4_step6.png"], "id": "random3_net6_base4"} | q+steps | [
"yes",
"no"
] |
|
414_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 3 as the base:
Step 1: Fold face 1 upwards
Step 2: Fold face 2 inwards towards face 3
Step 3: Fold face 5 downwards towards face 1
Step 4: Fold face 4 downwards towards face 3
Step 5: Fold face 6 inwards towards face 3
Based on the above steps, can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "2-2 net", "faces": {"3": [[0, 3, 0], [1, 3, 0], [1, 4, 0], [0, 4, 0]], "1": [[0.0, 3.0, 1.0], [1.0, 3.0, 1.0], [1.0, 3.0, 0.0], [0.0, 3.0, 0.0]], "2": [[1.0, 3.0, 1.0], [1.0, 4.0, 1.0], [1.0, 4.0, 0.0], [1.0, 3.0, 0.0]], "5": [[0.0, 3.0, 1.0], [0.0, 4.0, 1.0], [1.0, 4.0, 1.0], [1.0, 3.0, 1.0]], "4": [[0.0, 4.0, 1.0], [0.0, 4.0, 0.0], [1.0, 4.0, 0.0], [1.0, 4.0, 1.0]], "6": [[-6.123233995736766e-17, 3.0, 1.0], [-9.494107596574928e-16, 3.0, 0.0], [0.0, 4.0, 0.0], [0.0, 4.0, 1.0]]}, "face_connections": {"3": ["1"], "1": ["3", "2"], "2": ["1", "5"], "5": ["2", "4"], "4": ["5", "6"], "6": ["4"]}, "valid": true}, "base_face": "3", "folding_steps": [["1", "3", [0, 3, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["2", "1", [1.0, 3.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["5", "2", [1.0, 3.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "5", [0.0, 4.0, 1.0], [1.0, 0.0, 0.0], -1.5707963267948966], ["6", "4", [0.0, 4.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 2 inwards towards face 3", "Fold face 5 downwards towards face 1", "Fold face 4 downwards towards face 3", "Fold face 6 inwards towards face 3"], "images_per_step": ["output_dir/folding_nets/random3_net8_base3_step1.png", "output_dir/folding_nets/random3_net8_base3_step2.png", "output_dir/folding_nets/random3_net8_base3_step3.png", "output_dir/folding_nets/random3_net8_base3_step4.png", "output_dir/folding_nets/random3_net8_base3_step5.png", "output_dir/folding_nets/random3_net8_base3_step6.png"], "id": "random3_net8_base3"} | q+steps | [
"yes",
"no"
] |
|
122_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 5 as the base:
Step 1: Fold face 1 upwards
Step 2: Fold face 4 downwards
Step 3: Fold face 2 downwards towards face 6
Step 4: Fold face 3 upwards towards face 6
Step 5: Fold face 6 upwards towards face 4
Based on the above steps, can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "Linear 6-Face Row", "faces": {"6": [[0.9999999999999999, 0.0, 1.0], [1.0, 0.0, 0.0], [1.0, 1.0, 0.0], [0.9999999999999999, 1.0, 1.0]], "5": [[1, 0, 0], [2, 0, 0], [2, 1, 0], [1, 1, 0]], "1": [[2.0, 0.0, 0.0], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [2.0, 1.0, 0.0]], "4": [[2.0, 0.0, 1.0], [1.0, 0.0, 1.0], [1.0, 1.0, 1.0], [2.0, 1.0, 1.0]], "2": [[1.0, 0.0, 1.0], [0.9999999999999997, 0.0, 0.0], [0.9999999999999997, 1.0, 0.0], [1.0, 1.0, 1.0]], "3": [[0.9999999999999997, 0.0, 0.0], [1.9999999999999996, 0.0, -5.053215498074303e-16], [1.9999999999999996, 1.0, -5.053215498074303e-16], [0.9999999999999997, 1.0, 0.0]]}, "face_connections": {"6": ["5"], "5": ["6", "1"], "1": ["5", "4"], "4": ["1", "2"], "2": ["4", "3"], "3": ["2"]}, "valid": false}, "base_face": "5", "folding_steps": [["1", "5", [2, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "1", [2.0, 0.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["2", "4", [1.0, 0.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["3", "2", [0.9999999999999997, 0.0, 0.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["6", "5", [1, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 4 downwards", "Fold face 2 downwards towards face 6", "Fold face 3 upwards towards face 6", "Fold face 6 upwards towards face 4"], "images_per_step": ["output_dir/folding_nets/random2_net12_base5_step1.png", "output_dir/folding_nets/random2_net12_base5_step2.png", "output_dir/folding_nets/random2_net12_base5_step3.png"], "id": "random2_net12_base5"} | q+steps | [
"no",
"yes"
] |
|
183_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "invalid_G", "faces": {"1": [[0.0, 0.9999999999999999, 1.0], [1.0, 0.9999999999999999, 1.0], [1.0, 1.0, 0.0], [0.0, 1.0, 0.0]], "5": [[1.0, 0.9999999999999999, 1.0], [1.0, 2.0, 1.0], [1.0, 2.0, 1.1102230246251565e-16], [1.0, 1.0, 0.0]], "3": [[1.0, 2.0, 1.0], [0.0, 2.0000000000000004, 1.0000000000000002], [0.0, 2.0000000000000004, 2.220446049250313e-16], [1.0, 2.0, 1.1102230246251565e-16]], "2": [[0.0, 2.0000000000000004, 1.0000000000000002], [-6.123233995736766e-17, 1.0000000000000004, 1.0000000000000004], [-6.123233995736766e-17, 1.0000000000000004, 3.3306690738754696e-16], [0.0, 2.0000000000000004, 2.220446049250313e-16]], "4": [[0, 1, 0], [1, 1, 0], [1, 2, 0], [0, 2, 0]], "6": [[-1.232595164407831e-32, 2.0000000000000004, 2.220446049250313e-16], [-6.123233995736766e-17, 1.0000000000000004, 3.3306690738754696e-16], [0.9999999999999998, 1.0000000000000004, 2.718345674301793e-16], [0.9999999999999999, 2.0000000000000004, 1.6081226496766364e-16]]}, "face_connections": {"1": ["5", "4"], "5": ["1", "3"], "3": ["5", "2"], "2": ["3", "6"], "4": ["1"], "6": ["2"]}, "valid": false}, "base_face": "4", "folding_steps": [["1", "4", [0, 1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["5", "1", [1.0, 0.9999999999999999, 1.0], [0.0, 1.1102230246251565e-16, -1.0], -1.5707963267948966], ["3", "5", [1.0, 2.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["2", "3", [0.0, 2.0000000000000004, 1.0000000000000002], [0.0, 0.0, -1.0], -1.5707963267948966], ["6", "2", [-6.123233995736766e-17, 1.0000000000000004, 3.3306690738754696e-16], [6.123233995736766e-17, 1.0, -1.1102230246251565e-16], -1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 5 inwards towards face 4", "Fold face 3 inwards towards face 4", "Fold face 2 inwards towards face 1", "Fold face 6 upwards towards face 1"], "images_per_step": ["output_dir/folding_nets/random2_net20_base4_step1.png", "output_dir/folding_nets/random2_net20_base4_step2.png", "output_dir/folding_nets/random2_net20_base4_step3.png", "output_dir/folding_nets/random2_net20_base4_step4.png"], "id": "random2_net20_base4"} | q_only | [
"yes",
"no"
] |
|
367_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "Big T - Variant 1", "faces": {"1": [[0.9999999999999999, -2.0, 0.9999999999999998], [1.0, -3.0, 1.0000000000000002], [1.0, -3.0000000000000004, 2.220446049250313e-16], [0.9999999999999999, -2.0000000000000004, -2.220446049250313e-16]], "2": [[1.0, -3.0, 1.0000000000000002], [2.0, -3.0, 1.0000000000000002], [2.0, -3.0000000000000004, 2.220446049250313e-16], [1.0, -3.0000000000000004, 2.220446049250313e-16]], "3": [[2.0, -2.0, 1.0], [2.0, -2.0, 0.0], [2.0, -3.0, 2.220446049250313e-16], [2.0, -3.0, 1.0000000000000002]], "4": [[1.0, -2.0, 1.0], [2.0, -2.0, 1.0], [2.0, -3.0, 1.0000000000000002], [1.0, -3.0, 1.0000000000000002]], "5": [[1.0, -2.0, 0.0], [2.0, -2.0, 0.0], [2.0, -2.0, 1.0], [1.0, -2.0, 1.0]], "6": [[1, -3, 0], [2, -3, 0], [2, -2, 0], [1, -2, 0]]}, "face_connections": {"1": ["2"], "2": ["1", "4"], "3": ["4"], "4": ["2", "3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": true}, "base_face": "6", "folding_steps": [["5", "6", [2, -2, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["4", "5", [2.0, -2.0, 1.0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["3", "4", [2.0, -2.0, 1.0], [0.0, -1.0, 2.220446049250313e-16], -1.5707963267948966], ["2", "4", [2.0, -3.0, 1.0000000000000002], [-1.0, 0.0, 0.0], -1.5707963267948966], ["1", "2", [1.0, -3.0, 1.0000000000000002], [0.0, -4.440892098500626e-16, -1.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 5 upwards", "Fold face 4 downwards", "Fold face 3 downwards towards face 5", "Fold face 2 downwards towards face 3", "Fold face 1 downwards towards face 4"], "images_per_step": ["output_dir/folding_nets/net4_base6_step1.png", "output_dir/folding_nets/net4_base6_step2.png", "output_dir/folding_nets/net4_base6_step3.png", "output_dir/folding_nets/net4_base6_step4.png", "output_dir/folding_nets/net4_base6_step5.png", "output_dir/folding_nets/net4_base6_step6.png"], "id": "net4_base6"} | q_only | [
"yes",
"no"
] |
|
202_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=2)", "faces": {"2": [[4.0, 1.0, 0.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [4.0, 2.0, 0.0]], "4": [[4.0, 1.0, 1.0], [3.0, 1.0, 1.0], [3.0, 2.0, 1.0], [4.0, 2.0, 1.0]], "1": [[3.0, 1.0, 1.0], [3.0, 1.0, 0.0], [3.0, 2.0, 0.0], [3.0, 2.0, 1.0]], "3": [[3, 1, 0], [4, 1, 0], [4, 2, 0], [3, 2, 0]], "6": [[4.0, 1.0, 0.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [4.0, 2.0, 0.0]], "5": [[4.0, 0.9999999999999999, 1.0], [4.0, 0.9999999999999999, 0.0], [3.0, 1.0, 0.0], [3.0, 1.0, 1.0]]}, "face_connections": {"2": ["4"], "4": ["2", "1"], "1": ["4", "3", "5"], "3": ["1", "6"], "6": ["3"], "5": ["1"]}, "valid": false}, "base_face": "3", "folding_steps": [["1", "3", [3, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["5", "1", [3.0, 1.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["4", "1", [3.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "4", [4.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["6", "3", [4, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 5 inwards towards face 3", "Fold face 4 downwards towards face 5", "Fold face 2 downwards towards face 3", "Fold face 6 upwards towards face 2"], "images_per_step": ["output_dir/folding_nets/random1_net15_base3_step1.png", "output_dir/folding_nets/random1_net15_base3_step2.png", "output_dir/folding_nets/random1_net15_base3_step3.png", "output_dir/folding_nets/random1_net15_base3_step4.png"], "id": "random1_net15_base3"} | q_only | [
"no",
"yes"
] |
|
539_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 2 as the base:
Step 1: Fold face 3 upwards
Step 2: Fold face 5 downwards
Step 3: Fold face 1 downwards towards face 2
Step 4: Fold face 4 inwards towards face 5
Step 5: Fold face 6 upwards towards face 1
Based on the above steps, can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "invalid_G", "faces": {"1": [[4.0, 0.0, 0.0], [4.0, 0.0, 1.0], [4.0, 1.0, 1.0], [4.0, 1.0, 0.0]], "5": [[4.0, 0.0, 1.0], [3.0, 0.0, 1.0], [3.0, 1.0, 1.0], [4.0, 1.0, 1.0]], "3": [[3.0, 0.0, 1.0], [3.0, 0.0, 0.0], [3.0, 1.0, 0.0], [3.0, 1.0, 1.0]], "2": [[3, 0, 0], [4, 0, 0], [4, 1, 0], [3, 1, 0]], "4": [[4.0, 1.0, 0.0], [4.0, 1.0, 1.0], [3.0, 1.0, 1.0], [3.0, 1.0, 0.0]], "6": [[3.0, 1.0, 0.0], [4.0, 1.0, 0.0], [4.0, 1.0, 1.0], [3.0, 1.0, 1.0]]}, "face_connections": {"1": ["5", "4"], "5": ["1", "3"], "3": ["5", "2"], "2": ["3", "6"], "4": ["1"], "6": ["2"]}, "valid": false}, "base_face": "2", "folding_steps": [["3", "2", [3, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["5", "3", [3.0, 0.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["1", "5", [4.0, 0.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["4", "1", [4.0, 1.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["6", "2", [4, 1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 3 upwards", "Fold face 5 downwards", "Fold face 1 downwards towards face 2", "Fold face 4 inwards towards face 5", "Fold face 6 upwards towards face 1"], "images_per_step": ["output_dir/folding_nets/random2_net20_base2_step1.png", "output_dir/folding_nets/random2_net20_base2_step2.png", "output_dir/folding_nets/random2_net20_base2_step3.png", "output_dir/folding_nets/random2_net20_base2_step4.png"], "id": "random2_net20_base2"} | q+steps | [
"yes",
"no"
] |
|
273_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 3 as the base:
Step 1: Fold face 2 upwards
Step 2: Fold face 4 upwards towards face 2
Step 3: Fold face 5 inwards towards face 3
Step 4: Fold face 6 downwards towards face 2
Step 5: Fold face 1 inwards towards face 3
Based on the above steps, can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "2-2 net", "faces": {"1": [[0.9999999999999999, 3.0, 1.0], [1.0, 3.0, 0.0], [2.0, 3.0, 1.1102230246251565e-16], [2.0, 3.0, 1.0]], "2": [[0.9999999999999999, 2.0, 1.0], [1.0, 2.0, 0.0], [1.0, 3.0, 0.0], [0.9999999999999999, 3.0, 1.0]], "3": [[1, 2, 0], [2, 2, 0], [2, 3, 0], [1, 3, 0]], "4": [[1.0, 2.0, 1.0], [2.0, 2.0, 1.0], [2.0, 2.0, 0.0], [1.0, 2.0, 0.0]], "5": [[2.0, 2.0, 1.0], [2.0, 3.0, 1.0], [2.0, 3.0, 0.0], [2.0, 2.0, 0.0]], "6": [[1.0, 2.0, 1.0], [1.0, 3.0, 1.0000000000000004], [2.0, 3.0, 1.0], [2.0, 2.0, 1.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": true}, "base_face": "3", "folding_steps": [["2", "3", [1, 2, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["4", "3", [1, 2, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["5", "4", [2.0, 2.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["6", "5", [2.0, 2.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["1", "2", [1.0, 3.0, 0.0], [-1.1102230246251565e-16, 0.0, 1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 4 upwards towards face 2", "Fold face 5 inwards towards face 3", "Fold face 6 downwards towards face 2", "Fold face 1 inwards towards face 3"], "images_per_step": ["output_dir/folding_nets/net8_base3_step1.png", "output_dir/folding_nets/net8_base3_step2.png", "output_dir/folding_nets/net8_base3_step3.png", "output_dir/folding_nets/net8_base3_step4.png", "output_dir/folding_nets/net8_base3_step5.png", "output_dir/folding_nets/net8_base3_step6.png"], "id": "net8_base3"} | q+steps | [
"no",
"yes"
] |
|
331_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 1 as the base:
Step 1: Fold face 2 upwards
Step 2: Fold face 4 upwards towards face 2
Step 3: Fold face 6 downwards towards face 2
Step 4: Fold face 3 downwards towards face 2
Step 5: Fold face 5 inwards towards face 1
Based on the above steps, can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "Big T - Variant 3", "faces": {"2": [[0.9999999999999999, 0.0, 1.0], [1.0, 0.0, 0.0], [1.0, 1.0, 0.0], [0.9999999999999999, 1.0, 1.0]], "1": [[1, 0, 0], [2, 0, 0], [2, 1, 0], [1, 1, 0]], "5": [[2.0, 1.0, 2.220446049250313e-16], [2.0, 0.0, 1.1102230246251565e-16], [2.0, 0.0, 1.0], [2.0, 0.9999999999999999, 1.0000000000000002]], "4": [[1.0, -6.123233995736766e-17, 1.0], [2.0, -6.123233995736766e-17, 1.0], [2.0, 0.0, 0.0], [1.0, 0.0, 0.0]], "6": [[1.0, 0.9999999999999999, 1.0000000000000002], [2.0, 0.9999999999999999, 1.0000000000000002], [2.0, -6.123233995736766e-17, 1.0], [1.0, -6.123233995736766e-17, 1.0]], "3": [[1.0, 1.0, 2.220446049250313e-16], [2.0, 1.0, 2.220446049250313e-16], [2.0, 0.9999999999999999, 1.0000000000000002], [1.0, 0.9999999999999999, 1.0000000000000002]]}, "face_connections": {"2": ["1"], "1": ["2", "4"], "5": ["3"], "4": ["1", "6"], "6": ["4", "3"], "3": ["6", "5"]}, "valid": true}, "base_face": "1", "folding_steps": [["2", "1", [1, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["4", "1", [1, 0, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["6", "4", [1.0, -6.123233995736766e-17, 1.0], [1.0, 0.0, 0.0], -1.5707963267948966], ["3", "6", [1.0, 0.9999999999999999, 1.0000000000000002], [1.0, 0.0, 0.0], -1.5707963267948966], ["5", "3", [2.0, 1.0, 2.220446049250313e-16], [0.0, -1.1102230246251565e-16, 1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 4 upwards towards face 2", "Fold face 6 downwards towards face 2", "Fold face 3 downwards towards face 2", "Fold face 5 inwards towards face 1"], "images_per_step": ["output_dir/folding_nets/random1_net6_base1_step1.png", "output_dir/folding_nets/random1_net6_base1_step2.png", "output_dir/folding_nets/random1_net6_base1_step3.png", "output_dir/folding_nets/random1_net6_base1_step4.png", "output_dir/folding_nets/random1_net6_base1_step5.png", "output_dir/folding_nets/random1_net6_base1_step6.png"], "id": "random1_net6_base1"} | q+steps | [
"no",
"yes"
] |
|
529_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 1 as the base:
Step 1: Fold face 4 upwards
Step 2: Fold face 3 inwards towards face 1
Step 3: Fold face 2 downwards towards face 3
Step 4: Fold face 6 inwards towards face 1
Step 5: Fold face 5 downwards towards face 6
Based on the above steps, can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "t-shaped Net", "faces": {"4": [[0.0, 0.0, 0.0], [6.123233995736766e-17, 0.0, 1.0], [6.123233995736766e-17, 1.0, 1.0], [0.0, 1.0, 0.0]], "6": [[1.232595164407831e-32, 1.0, 0.0], [6.123233995736766e-17, 1.0, 1.0], [-0.9999999999999999, 1.0, 1.0], [-0.9999999999999999, 1.0, 1.1102230246251565e-16]], "1": [[-1, 0, 0], [0, 0, 0], [0, 1, 0], [-1, 1, 0]], "2": [[6.123233995736766e-17, 0.0, 1.0], [-0.9999999999999999, 0.0, 1.0000000000000002], [-0.9999999999999999, 1.0, 1.0000000000000002], [6.123233995736766e-17, 1.0, 1.0]], "5": [[-0.9999999999999999, 0.0, 1.0000000000000002], [-1.0, 0.0, 2.220446049250313e-16], [-1.0, 1.0, 2.220446049250313e-16], [-0.9999999999999999, 1.0, 1.0000000000000002]], "3": [[-1.0, -6.123233995736766e-17, 6.123233995736766e-17], [-0.9999999999999999, -6.123233995736766e-17, 1.0], [6.123233995736765e-17, 0.0, 1.0], [0.0, 0.0, 0.0]]}, "face_connections": {"6": ["4"], "1": ["4"], "4": ["6", "1", "2", "3"], "2": ["4", "5"], "5": ["2"], "3": ["4"]}, "valid": true}, "base_face": "1", "folding_steps": [["4", "1", [0, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["3", "4", [0.0, 0.0, 0.0], [6.123233995736766e-17, 0.0, 1.0], -1.5707963267948966], ["2", "4", [6.123233995736766e-17, 0.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["6", "4", [6.123233995736766e-17, 1.0, 1.0], [-6.123233995736766e-17, 0.0, -1.0], -1.5707963267948966], ["5", "2", [-0.9999999999999999, 0.0, 1.0000000000000002], [0.0, 1.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 4 upwards", "Fold face 3 inwards towards face 1", "Fold face 2 downwards towards face 3", "Fold face 6 inwards towards face 1", "Fold face 5 downwards towards face 6"], "images_per_step": ["output_dir/folding_nets/random1_net0_base1_step1.png", "output_dir/folding_nets/random1_net0_base1_step2.png", "output_dir/folding_nets/random1_net0_base1_step3.png", "output_dir/folding_nets/random1_net0_base1_step4.png", "output_dir/folding_nets/random1_net0_base1_step5.png", "output_dir/folding_nets/random1_net0_base1_step6.png"], "id": "random1_net0_base1"} | q+steps | [
"yes",
"no"
] |
|
237_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=4)", "faces": {"4": [[4.0, 1.0, -9.494107596574928e-16], [5.0, 1.0, 0.0], [5.0, 2.0, 0.0], [4.0, 2.0, -9.494107596574928e-16]], "5": [[5.0, 1.0, 0.0], [5.0, 1.0, 1.0], [5.0, 2.0, 1.0], [5.0, 2.0, 0.0]], "3": [[5.0, 1.0, 1.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [5.0, 2.0, 1.0]], "1": [[4.0, 1.0, 1.0], [4.0, 1.0, 0.0], [4.0, 2.0, 0.0], [4.0, 2.0, 1.0]], "6": [[4, 1, 0], [5, 1, 0], [5, 2, 0], [4, 2, 0]], "2": [[4.0, 0.9999999999999999, 1.0], [5.0, 0.9999999999999999, 1.0], [5.0, 1.0, 0.0], [4.0, 1.0, 0.0]]}, "face_connections": {"4": ["5"], "5": ["4", "3"], "3": ["5", "1"], "1": ["3", "6"], "6": ["1", "2"], "2": ["6"]}, "valid": false}, "base_face": "6", "folding_steps": [["1", "6", [4, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "6", [4, 1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["3", "1", [4.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["5", "3", [5.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["4", "5", [5.0, 1.0, 0.0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 2 upwards towards face 1", "Fold face 3 downwards towards face 2", "Fold face 5 downwards towards face 6", "Fold face 4 upwards towards face 1"], "images_per_step": ["output_dir/folding_nets/random1_net17_base6_step1.png", "output_dir/folding_nets/random1_net17_base6_step2.png", "output_dir/folding_nets/random1_net17_base6_step3.png", "output_dir/folding_nets/random1_net17_base6_step4.png"], "id": "random1_net17_base6"} | q_only | [
"yes",
"no"
] |
|
357_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=1)", "faces": {"6": [[4.0, 1.0, 0.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [4.0, 2.0, 0.0]], "5": [[4.0, 1.0, 1.0], [3.0, 1.0, 1.0], [3.0, 2.0, 1.0], [4.0, 2.0, 1.0]], "4": [[3.0, 1.0, 1.0], [3.0, 1.0, 0.0], [3.0, 2.0, 0.0], [3.0, 2.0, 1.0]], "3": [[3, 1, 0], [4, 1, 0], [4, 2, 0], [3, 2, 0]], "1": [[4.0, 1.0, 0.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [4.0, 2.0, 0.0]], "2": [[4.0, 0.9999999999999999, 0.0], [3.0, 0.9999999999999999, 0.0], [3.0, 1.0, 1.0], [4.0, 1.0, 1.0]]}, "face_connections": {"6": ["5"], "5": ["6", "4", "2"], "4": ["5", "3"], "3": ["4", "1"], "1": ["3"], "2": ["5"]}, "valid": false}, "base_face": "3", "folding_steps": [["1", "3", [4, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "3", [3, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["5", "4", [3.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "5", [4.0, 1.0, 1.0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["6", "5", [4.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 4 upwards", "Fold face 5 downwards towards face 1", "Fold face 2 downwards towards face 4", "Fold face 6 downwards towards face 3"], "images_per_step": ["output_dir/folding_nets/random3_net14_base3_step1.png", "output_dir/folding_nets/random3_net14_base3_step2.png", "output_dir/folding_nets/random3_net14_base3_step3.png"], "id": "random3_net14_base3"} | q_only | [
"no",
"yes"
] |
|
269_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 5 as the base:
Step 1: Fold face 2 upwards
Step 2: Fold face 1 inwards towards face 5
Step 3: Fold face 3 downwards towards face 1
Step 4: Fold face 4 downwards towards face 5
Step 5: Fold face 6 upwards towards face 2
Based on the above steps, can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=3)", "faces": {"6": [[4.0, 1.0, -9.494107596574928e-16], [5.0, 1.0, 0.0], [5.0, 2.0, 0.0], [4.0, 2.0, -9.494107596574928e-16]], "4": [[5.0, 1.0, 0.0], [5.0, 1.0, 1.0], [5.0, 2.0, 1.0], [5.0, 2.0, 0.0]], "3": [[5.0, 1.0, 1.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [5.0, 2.0, 1.0]], "2": [[4.0, 1.0, 1.0], [4.0, 1.0, 0.0], [4.0, 2.0, 0.0], [4.0, 2.0, 1.0]], "5": [[4, 1, 0], [5, 1, 0], [5, 2, 0], [4, 2, 0]], "1": [[5.0, 0.9999999999999999, 1.0], [5.0, 0.9999999999999999, 0.0], [4.0, 1.0, 0.0], [4.0, 1.0, 1.0]]}, "face_connections": {"6": ["4"], "4": ["6", "3"], "3": ["4", "2"], "2": ["3", "5", "1"], "5": ["2"], "1": ["2"]}, "valid": false}, "base_face": "5", "folding_steps": [["2", "5", [4, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["1", "2", [4.0, 1.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["3", "2", [4.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["4", "3", [5.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["6", "4", [5.0, 1.0, 0.0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 1 inwards towards face 5", "Fold face 3 downwards towards face 1", "Fold face 4 downwards towards face 5", "Fold face 6 upwards towards face 2"], "images_per_step": ["output_dir/folding_nets/random2_net16_base5_step1.png", "output_dir/folding_nets/random2_net16_base5_step2.png", "output_dir/folding_nets/random2_net16_base5_step3.png", "output_dir/folding_nets/random2_net16_base5_step4.png"], "id": "random2_net16_base5"} | q+steps | [
"yes",
"no"
] |
|
98_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 4 as the base:
Step 1: Fold face 2 upwards
Step 2: Fold face 5 inwards towards face 4
Step 3: Fold face 3 inwards towards face 4
Step 4: Fold face 1 downwards towards face 5
Step 5: Fold face 6 inwards towards face 1
Based on the above steps, can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "Big T - Variant 2", "faces": {"1": [[2.0, -0.9999999999999999, 1.0], [3.0, -0.9999999999999999, 1.0], [3.0, -2.0, 1.0], [2.0, -2.0, 1.0000000000000004]], "3": [[3.0, -0.9999999999999999, 1.0], [3.0, -0.9999999999999999, 0.0], [3.0, -2.0, 0.0], [3.0, -2.0, 1.0]], "4": [[2, -2, 0], [3, -2, 0], [3, -1, 0], [2, -1, 0]], "5": [[2.0, -1.0, 1.0], [2.0, -1.0, 0.0], [3.0, -0.9999999999999999, 0.0], [3.0, -0.9999999999999999, 1.0]], "2": [[2.0, -2.0, 1.0], [2.0, -2.0, 0.0], [2.0, -1.0, 0.0], [2.0, -1.0, 1.0]], "6": [[3.0, -2.0, 1.0], [3.0, -2.0, 0.0], [2.0, -2.0, 0.0], [2.0, -2.0, 1.0]]}, "face_connections": {"1": ["3"], "3": ["1", "5"], "4": ["2"], "5": ["3", "2"], "2": ["5", "4", "6"], "6": ["2"]}, "valid": true}, "base_face": "4", "folding_steps": [["2", "4", [2, -2, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["5", "2", [2.0, -1.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["3", "5", [3.0, -0.9999999999999999, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["1", "3", [3.0, -0.9999999999999999, 1.0], [0.0, -1.0, 0.0], 1.5707963267948966], ["6", "2", [2.0, -2.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 5 inwards towards face 4", "Fold face 3 inwards towards face 4", "Fold face 1 downwards towards face 5", "Fold face 6 inwards towards face 1"], "images_per_step": ["output_dir/folding_nets/random3_net5_base4_step1.png", "output_dir/folding_nets/random3_net5_base4_step2.png", "output_dir/folding_nets/random3_net5_base4_step3.png", "output_dir/folding_nets/random3_net5_base4_step4.png", "output_dir/folding_nets/random3_net5_base4_step5.png", "output_dir/folding_nets/random3_net5_base4_step6.png"], "id": "random3_net5_base4"} | q+steps | [
"yes",
"no"
] |
|
20_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 1 as the base:
Step 1: Fold face 5 upwards
Step 2: Fold face 4 upwards towards face 5
Step 3: Fold face 3 downwards towards face 4
Step 4: Fold face 2 downwards towards face 1
Step 5: Fold face 6 downwards towards face 1
Based on the above steps, can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "invalid_G", "faces": {"1": [[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0]], "5": [[1.0, 0.0, 0.0], [1.0, 0.0, 1.0], [1.0, 1.0, 1.0], [1.0, 1.0, 0.0]], "3": [[1.0, 0.0, 1.0], [0.0, 0.0, 1.0000000000000002], [0.0, 1.0, 1.0000000000000002], [1.0, 1.0, 1.0]], "2": [[0.0, 0.0, 1.0000000000000002], [-2.83276944882399e-16, 0.0, 2.220446049250313e-16], [-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [0.0, 1.0, 1.0000000000000002]], "4": [[0.0, 1.0, 0.0], [1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [0.0, 1.0, 1.0]], "6": [[-4.930380657631324e-32, 1.0, 1.0000000000000002], [-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [0.9999999999999997, 1.0, -6.123233995736767e-17], [0.9999999999999999, 1.0, 0.9999999999999999]]}, "face_connections": {"1": ["5", "4"], "5": ["1", "3"], "3": ["5", "2"], "2": ["3", "6"], "4": ["1"], "6": ["2"]}, "valid": false}, "base_face": "1", "folding_steps": [["5", "1", [1, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "1", [1, 1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["3", "5", [1.0, 0.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["2", "3", [0.0, 0.0, 1.0000000000000002], [0.0, 1.0, 0.0], -1.5707963267948966], ["6", "2", [-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [2.83276944882399e-16, 0.0, 1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 5 upwards", "Fold face 4 upwards towards face 5", "Fold face 3 downwards towards face 4", "Fold face 2 downwards towards face 1", "Fold face 6 downwards towards face 1"], "images_per_step": ["output_dir/folding_nets/random2_net20_base1_step1.png", "output_dir/folding_nets/random2_net20_base1_step2.png", "output_dir/folding_nets/random2_net20_base1_step3.png", "output_dir/folding_nets/random2_net20_base1_step4.png"], "id": "random2_net20_base1"} | q+steps | [
"no",
"yes"
] |
|
47_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 3 as the base:
Step 1: Fold face 5 upwards
Step 2: Fold face 2 downwards
Step 3: Fold face 1 upwards towards face 5
Step 4: Fold face 4 downwards towards face 3
Step 5: Fold face 6 downwards towards face 1
Based on the above steps, can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "Big T - Variant 2", "faces": {"1": [[0.9999999999999999, 0.0, 1.0], [1.0, 0.0, 0.0], [1.0, 1.0, 0.0], [0.9999999999999999, 1.0, 1.0]], "3": [[1, 0, 0], [2, 0, 0], [2, 1, 0], [1, 1, 0]], "4": [[2.0, 0.9999999999999999, 1.0000000000000002], [2.0, 1.0, 2.220446049250313e-16], [2.0, 1.1102230246251565e-16, 0.0], [2.0, -1.1102230246251565e-16, 1.0]], "5": [[1.0, -6.123233995736766e-17, 1.0], [2.0, -6.123233995736766e-17, 1.0], [2.0, 0.0, 0.0], [1.0, 0.0, 0.0]], "2": [[1.0, 0.9999999999999999, 1.0000000000000002], [2.0, 0.9999999999999999, 1.0000000000000002], [2.0, -6.123233995736766e-17, 1.0], [1.0, -6.123233995736766e-17, 1.0]], "6": [[1.0, 1.0, 2.220446049250313e-16], [2.0, 1.0, 2.220446049250313e-16], [2.0, 0.9999999999999999, 1.0000000000000002], [1.0, 0.9999999999999999, 1.0000000000000002]]}, "face_connections": {"1": ["3"], "3": ["1", "5"], "4": ["2"], "5": ["3", "2"], "2": ["5", "4", "6"], "6": ["2"]}, "valid": true}, "base_face": "3", "folding_steps": [["5", "3", [1, 0, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["2", "5", [1.0, -6.123233995736766e-17, 1.0], [1.0, 0.0, 0.0], -1.5707963267948966], ["1", "3", [1, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["4", "2", [2.0, 0.9999999999999999, 1.0000000000000002], [0.0, -1.0, -2.220446049250313e-16], -1.5707963267948966], ["6", "2", [1.0, 0.9999999999999999, 1.0000000000000002], [1.0, 0.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 5 upwards", "Fold face 2 downwards", "Fold face 1 upwards towards face 5", "Fold face 4 downwards towards face 3", "Fold face 6 downwards towards face 1"], "images_per_step": ["output_dir/folding_nets/random3_net5_base3_step1.png", "output_dir/folding_nets/random3_net5_base3_step2.png", "output_dir/folding_nets/random3_net5_base3_step3.png", "output_dir/folding_nets/random3_net5_base3_step4.png", "output_dir/folding_nets/random3_net5_base3_step5.png", "output_dir/folding_nets/random3_net5_base3_step6.png"], "id": "random3_net5_base3"} | q+steps | [
"no",
"yes"
] |
|
74_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 5 as the base:
Step 1: Fold face 1 upwards
Step 2: Fold face 4 inwards towards face 5
Step 3: Fold face 2 downwards towards face 1
Step 4: Fold face 3 downwards towards face 4
Step 5: Fold face 6 upwards towards face 3
Based on the above steps, can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "Invalid D", "faces": {"3": [[3.0000000000000004, 3.0000000000000004, 2.220446049250313e-16], [3.0000000000000004, 2.0, 0.0], [3.0, 2.0, 1.0], [3.0, 3.0, 1.0000000000000002]], "2": [[3.0, 3.0, 1.0000000000000002], [3.0, 2.0, 1.0], [2.0, 2.0, 1.0], [2.0, 3.0, 1.0000000000000002]], "4": [[3.0, 2.0, 1.0], [2.0, 2.0, 1.0], [2.0, 2.0, 0.0], [3.0, 2.0, 0.0]], "1": [[2.0, 2.0, 1.0], [2.0, 2.0, 0.0], [2.0, 3.0, 0.0], [2.0, 3.0, 1.0]], "5": [[2, 2, 0], [3, 2, 0], [3, 3, 0], [2, 3, 0]], "6": [[3.0, 2.0, 0.0], [3.0, 2.0, 1.0], [3.0, 3.0, 1.0], [3.0, 3.0, 0.0]]}, "face_connections": {"3": ["2"], "2": ["3", "4"], "4": ["2", "1"], "1": ["4", "5"], "5": ["1", "6"], "6": ["5"]}, "valid": false}, "base_face": "5", "folding_steps": [["1", "5", [2, 2, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["4", "1", [2.0, 2.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["2", "4", [3.0, 2.0, 1.0], [-1.0, 0.0, 0.0], 1.5707963267948966], ["3", "2", [3.0, 3.0, 1.0000000000000002], [0.0, -1.0, -2.220446049250313e-16], -1.5707963267948966], ["6", "5", [3, 2, 0], [0.0, 1.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 4 inwards towards face 5", "Fold face 2 downwards towards face 1", "Fold face 3 downwards towards face 4", "Fold face 6 upwards towards face 3"], "images_per_step": ["output_dir/folding_nets/random3_net19_base5_step1.png", "output_dir/folding_nets/random3_net19_base5_step2.png", "output_dir/folding_nets/random3_net19_base5_step3.png", "output_dir/folding_nets/random3_net19_base5_step4.png"], "id": "random3_net19_base5"} | q+steps | [
"yes",
"no"
] |
|
279_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 1 as the base:
Step 1: Fold face 2 upwards
Step 2: Fold face 5 inwards towards face 1
Step 3: Fold face 6 downwards towards face 5
Step 4: Fold face 4 downwards towards face 1
Step 5: Fold face 3 downwards towards face 2
Based on the above steps, can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "t-shaped Net Variant 2", "faces": {"2": [[0.0, 0.0, 0.0], [6.123233995736766e-17, 0.0, 1.0], [6.123233995736766e-17, 1.0, 1.0], [0.0, 1.0, 0.0]], "1": [[-1, 0, 0], [0, 0, 0], [0, 1, 0], [-1, 1, 0]], "6": [[6.123233995736766e-17, 0.0, 1.0], [-0.9999999999999999, 0.0, 1.0000000000000002], [-0.9999999999999999, 1.0, 1.0000000000000002], [6.123233995736766e-17, 1.0, 1.0]], "4": [[-0.9999999999999999, 0.0, 1.0000000000000002], [-1.0, 0.0, 2.220446049250313e-16], [-1.0, 1.0, 2.220446049250313e-16], [-0.9999999999999999, 1.0, 1.0000000000000002]], "5": [[-1.0, -6.123233995736766e-17, 6.123233995736766e-17], [-0.9999999999999999, -6.123233995736766e-17, 1.0], [6.123233995736765e-17, 0.0, 1.0], [0.0, 0.0, 0.0]], "3": [[-0.9999999999999999, 1.0, 1.0000000000000002], [-1.0, 1.0, 2.220446049250313e-16], [0.0, 1.0, 1.1102230246251565e-16], [0.0, 1.0, 1.0]]}, "face_connections": {"3": ["4"], "1": ["2"], "2": ["1", "6", "5"], "6": ["2", "4"], "4": ["3", "6"], "5": ["2"]}, "valid": true}, "base_face": "1", "folding_steps": [["2", "1", [0, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["5", "2", [0.0, 0.0, 0.0], [6.123233995736766e-17, 0.0, 1.0], -1.5707963267948966], ["6", "2", [6.123233995736766e-17, 0.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "6", [-0.9999999999999999, 0.0, 1.0000000000000002], [0.0, 1.0, 0.0], -1.5707963267948966], ["3", "4", [-1.0, 1.0, 2.220446049250313e-16], [1.1102230246251565e-16, 0.0, 1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 5 inwards towards face 1", "Fold face 6 downwards towards face 5", "Fold face 4 downwards towards face 1", "Fold face 3 downwards towards face 2"], "images_per_step": ["output_dir/folding_nets/random1_net2_base1_step1.png", "output_dir/folding_nets/random1_net2_base1_step2.png", "output_dir/folding_nets/random1_net2_base1_step3.png", "output_dir/folding_nets/random1_net2_base1_step4.png", "output_dir/folding_nets/random1_net2_base1_step5.png", "output_dir/folding_nets/random1_net2_base1_step6.png"], "id": "random1_net2_base1"} | q+steps | [
"yes",
"no"
] |
|
133_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=2)", "faces": {"1": [[0.9999999999999999, 1.0, 1.0], [1.0, 1.0, 0.0], [1.0, 2.0, 0.0], [0.9999999999999999, 2.0, 1.0]], "2": [[1, 1, 0], [2, 1, 0], [2, 2, 0], [1, 2, 0]], "3": [[2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [2.0, 2.0, 0.0]], "4": [[2.0, 1.0, 1.0], [1.0, 1.0, 1.0], [1.0, 2.0, 1.0], [2.0, 2.0, 1.0]], "5": [[1.0, 1.0, 1.0], [0.9999999999999997, 1.0, 0.0], [0.9999999999999997, 2.0, 0.0], [1.0, 2.0, 1.0]], "6": [[1.0, 0.9999999999999999, 0.0], [1.0, 0.9999999999999999, 1.0], [2.0, 1.0, 1.0], [2.0, 1.0, 0.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4", "6"], "4": ["3", "5"], "5": ["4"], "6": ["3"]}, "valid": false}, "base_face": "2", "folding_steps": [["1", "2", [1, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "2", [2, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "3", [2.0, 1.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["5", "4", [1.0, 1.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["6", "3", [2.0, 1.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 3 upwards", "Fold face 4 downwards towards face 1", "Fold face 5 downwards towards face 1", "Fold face 6 inwards towards face 1"], "images_per_step": ["output_dir/folding_nets/net15_base2_step1.png", "output_dir/folding_nets/net15_base2_step2.png", "output_dir/folding_nets/net15_base2_step3.png", "output_dir/folding_nets/net15_base2_step4.png"], "id": "net15_base2"} | q_only | [
"yes",
"no"
] |
|
452_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "Big T - Variant 2", "faces": {"5": [[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0]], "6": [[1.0, 0.0, 0.0], [1.0, 0.0, 1.0], [1.0, 1.0, 1.0], [1.0, 1.0, 0.0]], "2": [[-1.2246467991473532e-16, 0.9999999999999999, 1.0], [0.9999999999999999, 1.0, 1.0000000000000002], [1.0, 0.0, 1.0000000000000002], [-2.465190328815662e-32, -1.1102230246251565e-16, 1.0]], "4": [[0.0, -6.123233995736766e-17, 0.0], [0.0, -6.123233995736766e-17, 1.0], [1.0, 0.0, 1.0], [1.0, 0.0, 0.0]], "1": [[-1.2246467991473532e-16, 0.9999999999999999, 0.0], [-1.2246467991473532e-16, 0.9999999999999999, 1.0], [0.0, -6.123233995736766e-17, 1.0], [0.0, -6.123233995736766e-17, 0.0]], "3": [[0.9999999999999999, 1.0, 0.0], [0.9999999999999999, 1.0, 1.0], [-1.2246467991473532e-16, 0.9999999999999999, 1.0], [-1.2246467991473532e-16, 0.9999999999999999, 0.0]]}, "face_connections": {"5": ["6"], "6": ["5", "4"], "2": ["1"], "4": ["6", "1"], "1": ["4", "2", "3"], "3": ["1"]}, "valid": true}, "base_face": "5", "folding_steps": [["6", "5", [1, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "6", [1.0, 0.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["1", "4", [0.0, -6.123233995736766e-17, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["2", "1", [-1.2246467991473532e-16, 0.9999999999999999, 1.0], [1.2246467991473532e-16, -1.0, 0.0], -1.5707963267948966], ["3", "1", [-1.2246467991473532e-16, 0.9999999999999999, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 4 inwards towards face 5", "Fold face 1 inwards towards face 5", "Fold face 2 downwards towards face 6", "Fold face 3 inwards towards face 5"], "images_per_step": ["output_dir/folding_nets/random2_net5_base5_step1.png", "output_dir/folding_nets/random2_net5_base5_step2.png", "output_dir/folding_nets/random2_net5_base5_step3.png", "output_dir/folding_nets/random2_net5_base5_step4.png", "output_dir/folding_nets/random2_net5_base5_step5.png", "output_dir/folding_nets/random2_net5_base5_step6.png"], "id": "random2_net5_base5"} | q_only | [
"no",
"yes"
] |
|
219_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 5 as the base:
Step 1: Fold face 1 upwards
Step 2: Fold face 2 upwards towards face 1
Step 3: Fold face 4 inwards towards face 3
Step 4: Fold face 3 inwards towards face 5
Step 5: Fold face 6 downwards towards face 4
Based on the above steps, can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "Net H: Two rows with bottom row shifted right", "faces": {"4": [[0.9999999999999999, 0.0, 0.0], [1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [0.9999999999999999, 0.0, 1.0]], "1": [[1.0, 1.0, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [1.0, 1.0, 1.0]], "3": [[2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [2.0, 0.0, 1.0], [2.0, 0.0, 1.1102230246251565e-16]], "5": [[1, 0, 0], [2, 0, 0], [2, 1, 0], [1, 1, 0]], "2": [[2.0, 0.0, 0.0], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [2.0, 1.0, 0.0]], "6": [[2.0, 0.0, 1.0], [1.0, 0.0, 1.0], [1.0, 1.0, 1.0], [2.0, 1.0, 1.0]]}, "face_connections": {"4": ["1"], "1": ["4", "3", "5"], "3": ["1", "2"], "5": ["1", "2"], "2": ["3", "5", "6"], "6": ["2"]}, "valid": false}, "base_face": "5", "folding_steps": [["1", "5", [2, 1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["2", "5", [2, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "1", [1.0, 1.0, 0.0], [0.0, 0.0, 1.0], 1.5707963267948966], ["3", "2", [2.0, 1.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["6", "2", [2.0, 0.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 2 upwards towards face 1", "Fold face 4 inwards towards face 3", "Fold face 3 inwards towards face 5", "Fold face 6 downwards towards face 4"], "images_per_step": ["output_dir/folding_nets/random1_net23_base5_step1.png", "output_dir/folding_nets/random1_net23_base5_step2.png"], "id": "random1_net23_base5"} | q+steps | [
"no",
"yes"
] |
|
93_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 2 as the base:
Step 1: Fold face 5 upwards
Step 2: Fold face 3 upwards
Step 3: Fold face 6 inwards towards face 5
Step 4: Fold face 4 downwards towards face 5
Step 5: Fold face 1 downwards towards face 5
Based on the above steps, can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "3-3 Net", "faces": {"5": [[0.0, 2.0, 0.0], [1.0, 2.0, 0.0], [1.0, 2.0, 1.0], [0.0, 2.0, 1.0]], "2": [[0, 1, 0], [1, 1, 0], [1, 2, 0], [0, 2, 0]], "3": [[0.0, 0.9999999999999999, 1.0], [1.0, 0.9999999999999999, 1.0], [1.0, 1.0, 0.0], [0.0, 1.0, 0.0]], "6": [[1.0, 0.9999999999999999, 1.0], [1.0, 2.0, 1.0], [1.0, 2.0, 1.1102230246251565e-16], [1.0, 1.0, 0.0]], "4": [[0.0, 0.9999999999999998, 1.0], [0.0, 1.9999999999999998, 1.0], [1.0, 2.0, 1.0], [1.0, 0.9999999999999999, 1.0]], "1": [[-6.123233995736766e-17, 0.9999999999999997, 0.0], [-2.83276944882399e-16, 1.9999999999999996, 0.0], [0.0, 1.9999999999999998, 1.0], [0.0, 0.9999999999999998, 1.0]]}, "face_connections": {"5": ["2"], "2": ["5", "3"], "3": ["2", "6"], "6": ["3", "4"], "4": ["6", "1"], "1": ["4"]}, "valid": true}, "base_face": "2", "folding_steps": [["5", "2", [1, 2, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["3", "2", [0, 1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["6", "3", [1.0, 0.9999999999999999, 1.0], [0.0, 1.1102230246251565e-16, -1.0], -1.5707963267948966], ["4", "6", [1.0, 0.9999999999999999, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["1", "4", [0.0, 0.9999999999999998, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 5 upwards", "Fold face 3 upwards", "Fold face 6 inwards towards face 5", "Fold face 4 downwards towards face 5", "Fold face 1 downwards towards face 5"], "images_per_step": ["output_dir/folding_nets/random3_net7_base2_step1.png", "output_dir/folding_nets/random3_net7_base2_step2.png", "output_dir/folding_nets/random3_net7_base2_step3.png", "output_dir/folding_nets/random3_net7_base2_step4.png", "output_dir/folding_nets/random3_net7_base2_step5.png", "output_dir/folding_nets/random3_net7_base2_step6.png"], "id": "random3_net7_base2"} | q+steps | [
"yes",
"no"
] |
|
387_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 6 as the base:
Step 1: Fold face 5 upwards
Step 2: Fold face 2 upwards towards face 5
Step 3: Fold face 4 downwards towards face 5
Step 4: Fold face 1 downwards towards face 5
Step 5: Fold face 3 downwards towards face 6
Based on the above steps, can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "Big T - Variant 2", "faces": {"5": [[0.9999999999999999, 0.0, 1.0], [1.0, 0.0, 0.0], [1.0, 1.0, 0.0], [0.9999999999999999, 1.0, 1.0]], "6": [[1, 0, 0], [2, 0, 0], [2, 1, 0], [1, 1, 0]], "3": [[2.0, 0.9999999999999999, 1.0000000000000002], [2.0, 1.0, 2.220446049250313e-16], [2.0, 1.1102230246251565e-16, 0.0], [2.0, -1.1102230246251565e-16, 1.0]], "2": [[1.0, -6.123233995736766e-17, 1.0], [2.0, -6.123233995736766e-17, 1.0], [2.0, 0.0, 0.0], [1.0, 0.0, 0.0]], "4": [[1.0, 0.9999999999999999, 1.0000000000000002], [2.0, 0.9999999999999999, 1.0000000000000002], [2.0, -6.123233995736766e-17, 1.0], [1.0, -6.123233995736766e-17, 1.0]], "1": [[1.0, 1.0, 2.220446049250313e-16], [2.0, 1.0, 2.220446049250313e-16], [2.0, 0.9999999999999999, 1.0000000000000002], [1.0, 0.9999999999999999, 1.0000000000000002]]}, "face_connections": {"5": ["6"], "6": ["5", "2"], "3": ["4"], "2": ["6", "4"], "4": ["2", "3", "1"], "1": ["4"]}, "valid": true}, "base_face": "6", "folding_steps": [["5", "6", [1, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "6", [1, 0, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["4", "2", [1.0, -6.123233995736766e-17, 1.0], [1.0, 0.0, 0.0], -1.5707963267948966], ["1", "4", [1.0, 0.9999999999999999, 1.0000000000000002], [1.0, 0.0, 0.0], -1.5707963267948966], ["3", "4", [2.0, 0.9999999999999999, 1.0000000000000002], [0.0, -1.0, -2.220446049250313e-16], -1.5707963267948966]], "folding_step_descs": ["Fold face 5 upwards", "Fold face 2 upwards towards face 5", "Fold face 4 downwards towards face 5", "Fold face 1 downwards towards face 5", "Fold face 3 downwards towards face 6"], "images_per_step": ["output_dir/folding_nets/random1_net5_base6_step1.png", "output_dir/folding_nets/random1_net5_base6_step2.png", "output_dir/folding_nets/random1_net5_base6_step3.png", "output_dir/folding_nets/random1_net5_base6_step4.png", "output_dir/folding_nets/random1_net5_base6_step5.png", "output_dir/folding_nets/random1_net5_base6_step6.png"], "id": "random1_net5_base6"} | q+steps | [
"yes",
"no"
] |
|
446_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 3 as the base:
Step 1: Fold face 6 upwards
Step 2: Fold face 5 inwards towards face 3
Step 3: Fold face 2 inwards towards face 3
Step 4: Fold face 4 inwards towards face 5
Step 5: Fold face 1 inwards towards face 5
Based on the above steps, can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=1)", "faces": {"5": [[0.9999999999999999, 0.0, 0.0], [1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [0.9999999999999999, 0.0, 1.0]], "6": [[1.0, 1.0, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [1.0, 1.0, 1.0]], "2": [[2.0, 1.0, 0.0], [2.0, 0.0, 0.0], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0]], "4": [[2.0, 0.0, 0.0], [1.0, -6.123233995736766e-17, 0.0], [1.0, -6.123233995736766e-17, 1.0], [2.0, 0.0, 1.0]], "1": [[1.0, -6.123233995736766e-17, 0.0], [0.9999999999999999, 0.9999999999999999, 0.0], [0.9999999999999999, 0.9999999999999999, 1.0], [1.0, -6.123233995736766e-17, 1.0]], "3": [[1, 0, 0], [2, 0, 0], [2, 1, 0], [1, 1, 0]]}, "face_connections": {"5": ["6"], "6": ["5", "2", "3"], "2": ["6", "4"], "4": ["2", "1"], "1": ["4"], "3": ["6"]}, "valid": false}, "base_face": "3", "folding_steps": [["6", "3", [2, 1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["5", "6", [1.0, 1.0, 0.0], [0.0, 0.0, 1.0], 1.5707963267948966], ["2", "6", [2.0, 1.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["4", "2", [2.0, 0.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["1", "4", [1.0, -6.123233995736766e-17, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 5 inwards towards face 3", "Fold face 2 inwards towards face 3", "Fold face 4 inwards towards face 5", "Fold face 1 inwards towards face 5"], "images_per_step": ["output_dir/folding_nets/random2_net14_base3_step1.png", "output_dir/folding_nets/random2_net14_base3_step2.png", "output_dir/folding_nets/random2_net14_base3_step3.png", "output_dir/folding_nets/random2_net14_base3_step4.png"], "id": "random2_net14_base3"} | q+steps | [
"yes",
"no"
] |
|
484_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "invalid_E", "faces": {"4": [[0.0, 1.0, 0.0], [1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [0.0, 1.0, 1.0]], "3": [[-4.930380657631324e-32, 1.0, 1.0000000000000002], [-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [0.9999999999999997, 1.0, -6.123233995736767e-17], [0.9999999999999999, 1.0, 0.9999999999999999]], "1": [[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0]], "2": [[1.0, 0.0, 0.0], [1.0, 0.0, 1.0], [1.0, 1.0, 1.0], [1.0, 1.0, 0.0]], "6": [[1.0, 0.0, 1.0], [0.0, 0.0, 1.0000000000000002], [0.0, 1.0, 1.0000000000000002], [1.0, 1.0, 1.0]], "5": [[0.0, 0.0, 1.0000000000000002], [-2.83276944882399e-16, 0.0, 2.220446049250313e-16], [-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [0.0, 1.0, 1.0000000000000002]]}, "face_connections": {"4": ["1"], "3": ["5"], "1": ["4", "2"], "2": ["1", "6"], "6": ["2", "5"], "5": ["6", "3"]}, "valid": false}, "base_face": "1", "folding_steps": [["2", "1", [1, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "1", [1, 1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["6", "2", [1.0, 0.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["5", "6", [0.0, 0.0, 1.0000000000000002], [0.0, 1.0, 0.0], -1.5707963267948966], ["3", "5", [-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [2.83276944882399e-16, 0.0, 1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 4 upwards towards face 2", "Fold face 6 downwards towards face 4", "Fold face 5 downwards towards face 4", "Fold face 3 downwards towards face 4"], "images_per_step": ["output_dir/folding_nets/random1_net22_base1_step1.png", "output_dir/folding_nets/random1_net22_base1_step2.png", "output_dir/folding_nets/random1_net22_base1_step3.png", "output_dir/folding_nets/random1_net22_base1_step4.png"], "id": "random1_net22_base1"} | q_only | [
"yes",
"no"
] |
|
537_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 2 as the base:
Step 1: Fold face 5 upwards
Step 2: Fold face 4 upwards
Step 3: Fold face 6 downwards towards face 5
Step 4: Fold face 3 downwards towards face 2
Step 5: Fold face 1 upwards towards face 4
Based on the above steps, can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "Linear 6-Face Row", "faces": {"1": [[4.0, 0.0, -9.494107596574928e-16], [5.0, 0.0, 0.0], [5.0, 1.0, 0.0], [4.0, 1.0, -9.494107596574928e-16]], "3": [[5.0, 0.0, 0.0], [5.0, 0.0, 1.0], [5.0, 1.0, 1.0], [5.0, 1.0, 0.0]], "6": [[5.0, 0.0, 1.0], [4.0, 0.0, 1.0], [4.0, 1.0, 1.0], [5.0, 1.0, 1.0]], "4": [[4.0, 0.0, 1.0], [4.0, 0.0, 0.0], [4.0, 1.0, 0.0], [4.0, 1.0, 1.0]], "2": [[4, 0, 0], [5, 0, 0], [5, 1, 0], [4, 1, 0]], "5": [[5.0, 0.0, 0.0], [5.0, 0.0, 1.0], [5.0, 1.0, 1.0], [5.0, 1.0, 0.0]]}, "face_connections": {"1": ["3"], "3": ["1", "6"], "6": ["3", "4"], "4": ["6", "2"], "2": ["4", "5"], "5": ["2"]}, "valid": false}, "base_face": "2", "folding_steps": [["5", "2", [5, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "2", [4, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["6", "4", [4.0, 0.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "6", [5.0, 0.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["1", "3", [5.0, 0.0, 0.0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 5 upwards", "Fold face 4 upwards", "Fold face 6 downwards towards face 5", "Fold face 3 downwards towards face 2", "Fold face 1 upwards towards face 4"], "images_per_step": ["output_dir/folding_nets/random3_net12_base2_step1.png", "output_dir/folding_nets/random3_net12_base2_step2.png", "output_dir/folding_nets/random3_net12_base2_step3.png"], "id": "random3_net12_base2"} | q+steps | [
"no",
"yes"
] |
|
158_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "Linear 6-Face Row", "faces": {"3": [[4.0, 0.0, -9.494107596574928e-16], [5.0, 0.0, 0.0], [5.0, 1.0, 0.0], [4.0, 1.0, -9.494107596574928e-16]], "2": [[5.0, 0.0, 0.0], [5.0, 0.0, 1.0], [5.0, 1.0, 1.0], [5.0, 1.0, 0.0]], "5": [[5.0, 0.0, 1.0], [4.0, 0.0, 1.0], [4.0, 1.0, 1.0], [5.0, 1.0, 1.0]], "1": [[4.0, 0.0, 1.0], [4.0, 0.0, 0.0], [4.0, 1.0, 0.0], [4.0, 1.0, 1.0]], "4": [[4, 0, 0], [5, 0, 0], [5, 1, 0], [4, 1, 0]], "6": [[5.0, 0.0, 0.0], [5.0, 0.0, 1.0], [5.0, 1.0, 1.0], [5.0, 1.0, 0.0]]}, "face_connections": {"3": ["2"], "2": ["3", "5"], "5": ["2", "1"], "1": ["5", "4"], "4": ["1", "6"], "6": ["4"]}, "valid": false}, "base_face": "4", "folding_steps": [["1", "4", [4, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["5", "1", [4.0, 0.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "5", [5.0, 0.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "2", [5.0, 0.0, 0.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["6", "4", [5, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 5 downwards", "Fold face 2 downwards towards face 4", "Fold face 3 upwards towards face 1", "Fold face 6 upwards towards face 3"], "images_per_step": ["output_dir/folding_nets/random1_net12_base4_step1.png", "output_dir/folding_nets/random1_net12_base4_step2.png", "output_dir/folding_nets/random1_net12_base4_step3.png"], "id": "random1_net12_base4"} | q_only | [
"yes",
"no"
] |
|
502_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 1 as the base:
Step 1: Fold face 3 upwards
Step 2: Fold face 2 inwards towards face 1
Step 3: Fold face 5 downwards towards face 3
Step 4: Fold face 4 downwards towards face 2
Step 5: Fold face 6 downwards towards face 5
Based on the above steps, can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "2-2 net", "faces": {"6": [[3.0, -2.8327694488239893e-16, 2.220446049250313e-16], [3.0, 0.0, 1.0000000000000002], [3.0, 1.0, 1.0000000000000002], [3.0, 0.9999999999999997, 2.220446049250313e-16]], "4": [[2.0000000000000004, -2.83276944882399e-16, 0.0], [2.0, 0.0, 1.0], [3.0, 0.0, 1.0000000000000002], [3.0, -2.83276944882399e-16, 2.220446049250313e-16]], "5": [[2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [3.0, 1.0, 1.0000000000000002], [3.0, 0.0, 1.0000000000000002]], "2": [[2.0, 0.0, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [2.0, 0.0, 1.0]], "3": [[2.0, 1.0, 0.0], [3.0, 1.0, 0.0], [3.0, 1.0, 1.0], [2.0, 1.0, 1.0]], "1": [[2, 0, 0], [3, 0, 0], [3, 1, 0], [2, 1, 0]]}, "face_connections": {"6": ["4"], "4": ["6", "5"], "5": ["4", "2"], "2": ["5", "3"], "3": ["2", "1"], "1": ["3"]}, "valid": true}, "base_face": "1", "folding_steps": [["3", "1", [3, 1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["2", "3", [2.0, 1.0, 0.0], [0.0, 0.0, 1.0], 1.5707963267948966], ["5", "2", [2.0, 1.0, 1.0], [0.0, -1.0, 0.0], -1.5707963267948966], ["4", "5", [2.0, 0.0, 1.0], [1.0, 0.0, 2.220446049250313e-16], 1.5707963267948966], ["6", "4", [3.0, 0.0, 1.0000000000000002], [0.0, -2.83276944882399e-16, -1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 3 upwards", "Fold face 2 inwards towards face 1", "Fold face 5 downwards towards face 3", "Fold face 4 downwards towards face 2", "Fold face 6 downwards towards face 5"], "images_per_step": ["output_dir/folding_nets/random2_net8_base1_step1.png", "output_dir/folding_nets/random2_net8_base1_step2.png", "output_dir/folding_nets/random2_net8_base1_step3.png", "output_dir/folding_nets/random2_net8_base1_step4.png", "output_dir/folding_nets/random2_net8_base1_step5.png", "output_dir/folding_nets/random2_net8_base1_step6.png"], "id": "random2_net8_base1"} | q+steps | [
"no",
"yes"
] |
|
90_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 4 as the base:
Step 1: Fold face 5 upwards
Step 2: Fold face 2 upwards
Step 3: Fold face 6 downwards towards face 5
Step 4: Fold face 3 downwards towards face 4
Step 5: Fold face 1 inwards towards face 6
Based on the above steps, can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=0)", "faces": {"3": [[4.0, 1.0, 0.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [4.0, 2.0, 0.0]], "6": [[4.0, 1.0, 1.0], [3.0, 1.0, 1.0], [3.0, 2.0, 1.0], [4.0, 2.0, 1.0]], "2": [[3.0, 1.0, 1.0], [3.0, 1.0, 0.0], [3.0, 2.0, 0.0], [3.0, 2.0, 1.0]], "4": [[3, 1, 0], [4, 1, 0], [4, 2, 0], [3, 2, 0]], "5": [[4.0, 1.0, 0.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [4.0, 2.0, 0.0]], "1": [[3.0, 0.9999999999999999, 0.0], [3.0, 0.9999999999999999, 1.0], [4.0, 1.0, 1.0], [4.0, 1.0, 0.0]]}, "face_connections": {"3": ["6", "1"], "6": ["3", "2"], "2": ["6", "4"], "4": ["2", "5"], "5": ["4"], "1": ["3"]}, "valid": false}, "base_face": "4", "folding_steps": [["5", "4", [4, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["2", "4", [3, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["6", "2", [3.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "6", [4.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["1", "3", [4.0, 1.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 5 upwards", "Fold face 2 upwards", "Fold face 6 downwards towards face 5", "Fold face 3 downwards towards face 4", "Fold face 1 inwards towards face 6"], "images_per_step": ["output_dir/folding_nets/random1_net13_base4_step1.png", "output_dir/folding_nets/random1_net13_base4_step2.png", "output_dir/folding_nets/random1_net13_base4_step3.png"], "id": "random1_net13_base4"} | q+steps | [
"yes",
"no"
] |
|
388_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 6 as the base:
Step 1: Fold face 1 upwards
Step 2: Fold face 2 inwards towards face 6
Step 3: Fold face 5 inwards towards face 6
Step 4: Fold face 4 inwards towards face 5
Step 5: Fold face 3 downwards towards face 5
Based on the above steps, can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "t-shaped Net Variant 1", "faces": {"2": [[0.9999999999999999, 2.0, 1.0], [1.0, 0.9999999999999999, 1.0], [1.0, 1.0, 0.0], [0.9999999999999999, 2.0, 1.1102230246251565e-16]], "5": [[2.0, 2.0, 1.0000000000000002], [0.9999999999999999, 2.0, 1.0], [0.9999999999999999, 2.0, 1.1102230246251565e-16], [2.0, 2.0, 2.220446049250313e-16]], "1": [[1.0, 0.9999999999999999, 1.0], [2.0, 0.9999999999999999, 1.0], [2.0, 1.0, 0.0], [1.0, 1.0, 0.0]], "4": [[2.0, 0.9999999999999999, 1.0], [2.0, 2.0, 1.0], [2.0, 2.0, 1.1102230246251565e-16], [2.0, 1.0, 0.0]], "3": [[2.0, 2.0, 1.0], [2.0, 1.0, 1.0], [1.0, 1.0, 1.0], [0.9999999999999999, 2.0, 1.0]], "6": [[1, 1, 0], [2, 1, 0], [2, 2, 0], [1, 2, 0]]}, "face_connections": {"6": ["1"], "5": ["2"], "2": ["5", "1", "3"], "1": ["6", "2", "4"], "4": ["1"], "3": ["2"]}, "valid": true}, "base_face": "6", "folding_steps": [["1", "6", [1, 1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["2", "1", [1.0, 0.9999999999999999, 1.0], [0.0, 1.1102230246251565e-16, -1.0], 1.5707963267948966], ["5", "2", [0.9999999999999999, 2.0, 1.0], [0.0, 0.0, -1.0], 1.5707963267948966], ["4", "1", [2.0, 0.9999999999999999, 1.0], [0.0, 1.1102230246251565e-16, -1.0], -1.5707963267948966], ["3", "2", [0.9999999999999999, 2.0, 1.0], [1.1102230246251565e-16, -1.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 2 inwards towards face 6", "Fold face 5 inwards towards face 6", "Fold face 4 inwards towards face 5", "Fold face 3 downwards towards face 5"], "images_per_step": ["output_dir/folding_nets/random1_net1_base6_step1.png", "output_dir/folding_nets/random1_net1_base6_step2.png", "output_dir/folding_nets/random1_net1_base6_step3.png", "output_dir/folding_nets/random1_net1_base6_step4.png", "output_dir/folding_nets/random1_net1_base6_step5.png", "output_dir/folding_nets/random1_net1_base6_step6.png"], "id": "random1_net1_base6"} | q+steps | [
"no",
"yes"
] |
|
471_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "Net H: Two rows with bottom row shifted right", "faces": {"6": [[3.0, 1.0, 1.0000000000000002], [2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [3.0, 2.0, 1.0000000000000002]], "4": [[2.0, 1.0, 1.0], [2.0, 1.0, 0.0], [2.0, 2.0, 0.0], [2.0, 2.0, 1.0]], "1": [[2, 1, 0], [3, 1, 0], [3, 2, 0], [2, 2, 0]], "3": [[2.0, 2.0, 1.0], [2.0, 2.0, 1.1102230246251565e-16], [2.0, 1.0, 0.0], [2.0, 1.0, 1.0]], "2": [[2.0, 0.9999999999999999, 1.0], [3.0, 0.9999999999999999, 1.0], [3.0, 1.0, 0.0], [2.0, 1.0, 0.0]], "5": [[3.0, 0.9999999999999999, 1.0], [3.0, 2.0, 1.0], [3.0, 2.0, 1.1102230246251565e-16], [3.0, 1.0, 0.0]]}, "face_connections": {"6": ["4"], "4": ["6", "1", "3"], "1": ["4", "2"], "3": ["4", "2"], "2": ["1", "3", "5"], "5": ["2"]}, "valid": false}, "base_face": "1", "folding_steps": [["2", "1", [2, 1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["5", "2", [3.0, 0.9999999999999999, 1.0], [0.0, 1.1102230246251565e-16, -1.0], -1.5707963267948966], ["4", "1", [2, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "4", [2.0, 1.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["6", "4", [2.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 5 inwards towards face 1", "Fold face 4 upwards towards face 2", "Fold face 3 inwards towards face 6", "Fold face 6 downwards towards face 3"], "images_per_step": ["output_dir/folding_nets/random3_net23_base1_step1.png", "output_dir/folding_nets/random3_net23_base1_step2.png", "output_dir/folding_nets/random3_net23_base1_step3.png"], "id": "random3_net23_base1"} | q_only | [
"yes",
"no"
] |
|
445_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "Net H: Two rows with bottom row shifted right", "faces": {"1": [[0, 1, 0], [1, 1, 0], [1, 2, 0], [0, 2, 0]], "2": [[1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [1.0, 2.0, 1.0], [1.0, 2.0, 0.0]], "3": [[1.0, 1.0, 1.0], [1.0, 0.9999999999999998, 2.0], [1.0, 1.9999999999999998, 2.0], [1.0, 2.0, 1.0000000000000002]], "4": [[0.0, 0.9999999999999999, 0.0], [0.0, 0.9999999999999999, 1.0], [1.0, 1.0, 1.0], [1.0, 1.0, 0.0]], "5": [[1.0, 0.0, 0.9999999999999998], [1.0, -2.220446049250313e-16, 1.9999999999999998], [0.0, -1.6081226496766364e-16, 1.9999999999999998], [0.0, 6.123233995736766e-17, 0.9999999999999998]], "6": [[1.0, -2.220446049250313e-16, 1.9999999999999998], [1.0, 1.0, 2.0000000000000004], [1.1102230246251565e-16, 0.9999999999999997, 2.0000000000000004], [0.0, -1.6081226496766364e-16, 1.9999999999999998]]}, "face_connections": {"1": ["2"], "2": ["1", "3", "4"], "3": ["2", "5"], "4": ["2", "5"], "5": ["3", "4", "6"], "6": ["5"]}, "valid": false}, "base_face": "1", "folding_steps": [["2", "1", [1, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "2", [1.0, 1.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["3", "2", [1.0, 1.0, 1.0], [0.0, -2.220446049250313e-16, 1.0], 1.5707963267948966], ["5", "4", [1.0, 0.0, 0.9999999999999998], [0.0, -2.220446049250313e-16, 1.0], 1.5707963267948966], ["6", "5", [1.0, -2.220446049250313e-16, 1.9999999999999998], [-1.0, 6.123233995736767e-17, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 4 inwards towards face 1", "Fold face 3 inwards", "Fold face 5 downwards", "Fold face 6 downwards"], "images_per_step": ["output_dir/folding_nets/net23_base1_step1.png", "output_dir/folding_nets/net23_base1_step2.png"], "id": "net23_base1"} | q_only | [
"yes",
"no"
] |
|
433_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "2 Rows of 3", "faces": {"6": [[0.9999999999999999, 1.0, 1.0], [1.0, 1.0, 0.0], [0.9999999999999998, 2.0, -1.232595164407831e-32], [0.9999999999999997, 2.0, 1.0]], "5": [[1, 1, 0], [2, 1, 0], [2, 2, 0], [1, 2, 0]], "2": [[2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [2.0, 2.0, 0.0]], "4": [[0.9999999999999999, 2.0, 1.0], [1.0, 0.9999999999999999, 1.0], [1.0, 1.0, 0.0], [0.9999999999999999, 2.0, 1.1102230246251565e-16]], "3": [[1.0, 0.9999999999999999, 1.0], [2.0, 0.9999999999999999, 1.0], [2.0, 1.0, 0.0], [1.0, 1.0, 0.0]], "1": [[1.0, 0.9999999999999999, 0.0], [1.0, 0.9999999999999999, 1.0], [2.0, 1.0, 1.0], [2.0, 1.0, 0.0]]}, "face_connections": {"6": ["5", "4"], "5": ["6", "2", "3"], "2": ["5", "1"], "4": ["6", "3"], "3": ["5", "4", "1"], "1": ["2", "3"]}, "valid": false}, "base_face": "5", "folding_steps": [["2", "5", [2, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["1", "2", [2.0, 1.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["3", "5", [1, 1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["4", "3", [1.0, 0.9999999999999999, 1.0], [0.0, 1.1102230246251565e-16, -1.0], 1.5707963267948966], ["6", "4", [1.0, 1.0, 0.0], [-1.1102230246251565e-16, 1.0, 1.1102230246251565e-16], 1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 1 inwards towards face 5", "Fold face 3 upwards towards face 2", "Fold face 4 inwards towards face 5", "Fold face 6 upwards towards face 3"], "images_per_step": ["output_dir/folding_nets/random2_net18_base5_step1.png", "output_dir/folding_nets/random2_net18_base5_step2.png"], "id": "random2_net18_base5"} | q_only | [
"no",
"yes"
] |
|
4_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "2-2 net", "faces": {"5": [[3.0, 1.0, 1.0000000000000004], [3.0, 2.0, 1.0], [3.0, 1.9999999999999996, 0.0], [3.0, 0.9999999999999996, 4.440892098500626e-16]], "4": [[2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [3.0, 2.0, 1.0], [3.0, 1.0, 1.0000000000000004]], "6": [[2.0, 2.0, 1.0], [2.0, 2.0, 0.0], [3.0, 2.0, 0.0], [3.0, 2.0, 1.0]], "2": [[2.0, 1.0, 1.0], [2.0, 1.0, 0.0], [2.0, 2.0, 0.0], [2.0, 2.0, 1.0]], "1": [[2, 1, 0], [3, 1, 0], [3, 2, 0], [2, 2, 0]], "3": [[2.0, 0.9999999999999999, 1.0], [3.0, 0.9999999999999999, 1.0], [3.0, 1.0, 0.0], [2.0, 1.0, 0.0]]}, "face_connections": {"5": ["4"], "4": ["5", "6"], "6": ["4", "2"], "2": ["6", "1"], "1": ["2", "3"], "3": ["1"]}, "valid": true}, "base_face": "1", "folding_steps": [["2", "1", [2, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "1", [2, 1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["6", "2", [2.0, 2.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["4", "6", [2.0, 2.0, 1.0], [1.0, 0.0, 0.0], 1.5707963267948966], ["5", "4", [3.0, 2.0, 1.0], [0.0, -1.0, 4.440892098500626e-16], -1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 3 upwards towards face 2", "Fold face 6 inwards towards face 1", "Fold face 4 downwards towards face 2", "Fold face 5 downwards towards face 6"], "images_per_step": ["output_dir/folding_nets/random1_net8_base1_step1.png", "output_dir/folding_nets/random1_net8_base1_step2.png", "output_dir/folding_nets/random1_net8_base1_step3.png", "output_dir/folding_nets/random1_net8_base1_step4.png", "output_dir/folding_nets/random1_net8_base1_step5.png", "output_dir/folding_nets/random1_net8_base1_step6.png"], "id": "random1_net8_base1"} | q_only | [
"no",
"yes"
] |
|
110_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 4 as the base:
Step 1: Fold face 3 upwards
Step 2: Fold face 2 downwards
Step 3: Fold face 5 upwards towards face 1
Step 4: Fold face 6 inwards towards face 2
Step 5: Fold face 1 downwards towards face 4
Based on the above steps, can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=4)", "faces": {"1": [[4.0, 1.0, 0.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [4.0, 2.0, 0.0]], "2": [[4.0, 1.0, 1.0], [3.0, 1.0, 1.0], [3.0, 2.0, 1.0], [4.0, 2.0, 1.0]], "3": [[3.0, 1.0, 1.0], [3.0, 1.0, 0.0], [3.0, 2.0, 0.0], [3.0, 2.0, 1.0]], "4": [[3, 1, 0], [4, 1, 0], [4, 2, 0], [3, 2, 0]], "5": [[4.0, 1.0, 0.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [4.0, 2.0, 0.0]], "6": [[3.0, 0.9999999999999999, 0.0], [3.0, 0.9999999999999999, 1.0], [4.0, 1.0, 1.0], [4.0, 1.0, 0.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": false}, "base_face": "4", "folding_steps": [["3", "4", [3, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "3", [3.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["5", "4", [4, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["6", "5", [4.0, 1.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["1", "2", [4.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 3 upwards", "Fold face 2 downwards", "Fold face 5 upwards towards face 1", "Fold face 6 inwards towards face 2", "Fold face 1 downwards towards face 4"], "images_per_step": ["output_dir/folding_nets/net17_base4_step1.png", "output_dir/folding_nets/net17_base4_step2.png", "output_dir/folding_nets/net17_base4_step3.png", "output_dir/folding_nets/net17_base4_step4.png"], "id": "net17_base4"} | q+steps | [
"yes",
"no"
] |
|
122_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "Linear 6-Face Row", "faces": {"6": [[0.9999999999999999, 0.0, 1.0], [1.0, 0.0, 0.0], [1.0, 1.0, 0.0], [0.9999999999999999, 1.0, 1.0]], "5": [[1, 0, 0], [2, 0, 0], [2, 1, 0], [1, 1, 0]], "1": [[2.0, 0.0, 0.0], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [2.0, 1.0, 0.0]], "4": [[2.0, 0.0, 1.0], [1.0, 0.0, 1.0], [1.0, 1.0, 1.0], [2.0, 1.0, 1.0]], "2": [[1.0, 0.0, 1.0], [0.9999999999999997, 0.0, 0.0], [0.9999999999999997, 1.0, 0.0], [1.0, 1.0, 1.0]], "3": [[0.9999999999999997, 0.0, 0.0], [1.9999999999999996, 0.0, -5.053215498074303e-16], [1.9999999999999996, 1.0, -5.053215498074303e-16], [0.9999999999999997, 1.0, 0.0]]}, "face_connections": {"6": ["5"], "5": ["6", "1"], "1": ["5", "4"], "4": ["1", "2"], "2": ["4", "3"], "3": ["2"]}, "valid": false}, "base_face": "5", "folding_steps": [["1", "5", [2, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "1", [2.0, 0.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["2", "4", [1.0, 0.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["3", "2", [0.9999999999999997, 0.0, 0.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["6", "5", [1, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 4 downwards", "Fold face 2 downwards towards face 6", "Fold face 3 upwards towards face 6", "Fold face 6 upwards towards face 4"], "images_per_step": ["output_dir/folding_nets/random2_net12_base5_step1.png", "output_dir/folding_nets/random2_net12_base5_step2.png", "output_dir/folding_nets/random2_net12_base5_step3.png"], "id": "random2_net12_base5"} | q_only | [
"no",
"yes"
] |
|
522_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 4 as the base:
Step 1: Fold face 1 upwards
Step 2: Fold face 2 inwards towards face 4
Step 3: Fold face 3 inwards towards face 4
Step 4: Fold face 5 upwards towards face 1
Step 5: Fold face 6 inwards
Based on the above steps, can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "2 Rows of 3", "faces": {"1": [[0.0, 1.0, 0.0], [1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [0.0, 1.0, 1.0]], "2": [[1.0, 1.0, 0.0], [1.0, 0.0, 0.0], [1.0, 0.0, 1.0], [1.0, 1.0, 1.0]], "3": [[1.0, 0.0, 0.0], [0.0, -2.83276944882399e-16, 0.0], [0.0, -2.83276944882399e-16, 1.0], [1.0, 0.0, 1.0]], "4": [[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0]], "5": [[1.0, 0.0, 0.0], [1.0, 0.0, 1.0], [1.0, 1.0, 1.0], [1.0, 1.0, 0.0]], "6": [[2.0, 0.0, -6.123233995736766e-17], [2.0, 0.0, -1.0], [1.9999999999999998, 1.0, -1.0], [2.0, 1.0, 0.0]]}, "face_connections": {"1": ["2", "4"], "2": ["1", "3", "5"], "3": ["2", "6"], "4": ["1", "5"], "5": ["2", "4", "6"], "6": ["3", "5"]}, "valid": false}, "base_face": "4", "folding_steps": [["1", "4", [1, 1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["2", "1", [1.0, 1.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["3", "2", [1.0, 0.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["5", "2", [1.0, 1.0, 0.0], [0.0, -1.0, 0.0], 1.5707963267948966], ["6", "5", [2.0, 0.0, -6.123233995736766e-17], [0.0, 0.0, -1.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 2 inwards towards face 4", "Fold face 3 inwards towards face 4", "Fold face 5 upwards towards face 1", "Fold face 6 inwards"], "images_per_step": ["output_dir/folding_nets/net18_base4_step1.png", "output_dir/folding_nets/net18_base4_step2.png"], "id": "net18_base4"} | q+steps | [
"no",
"yes"
] |
|
86_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "3-3 Net", "faces": {"1": [[0.0, 2.0, 0.0], [1.0, 2.0, 0.0], [1.0, 2.0, 1.0], [0.0, 2.0, 1.0]], "2": [[0, 1, 0], [1, 1, 0], [1, 2, 0], [0, 2, 0]], "3": [[0.0, 0.9999999999999999, 1.0], [1.0, 0.9999999999999999, 1.0], [1.0, 1.0, 0.0], [0.0, 1.0, 0.0]], "4": [[1.0, 0.9999999999999999, 1.0], [1.0, 2.0, 1.0], [1.0, 2.0, 1.1102230246251565e-16], [1.0, 1.0, 0.0]], "5": [[0.0, 0.9999999999999998, 1.0], [0.0, 1.9999999999999998, 1.0], [1.0, 2.0, 1.0], [1.0, 0.9999999999999999, 1.0]], "6": [[-6.123233995736766e-17, 0.9999999999999997, 0.0], [-2.83276944882399e-16, 1.9999999999999996, 0.0], [0.0, 1.9999999999999998, 1.0], [0.0, 0.9999999999999998, 1.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": true}, "base_face": "2", "folding_steps": [["1", "2", [1, 2, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["3", "2", [0, 1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["4", "3", [1.0, 0.9999999999999999, 1.0], [0.0, 1.1102230246251565e-16, -1.0], -1.5707963267948966], ["5", "4", [1.0, 0.9999999999999999, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["6", "5", [0.0, 0.9999999999999998, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 3 upwards", "Fold face 4 inwards towards face 1", "Fold face 5 downwards towards face 1", "Fold face 6 downwards towards face 1"], "images_per_step": ["output_dir/folding_nets/net7_base2_step1.png", "output_dir/folding_nets/net7_base2_step2.png", "output_dir/folding_nets/net7_base2_step3.png", "output_dir/folding_nets/net7_base2_step4.png", "output_dir/folding_nets/net7_base2_step5.png", "output_dir/folding_nets/net7_base2_step6.png"], "id": "net7_base2"} | q_only | [
"no",
"yes"
] |
|
567_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 3 as the base:
Step 1: Fold face 1 upwards
Step 2: Fold face 2 upwards
Step 3: Fold face 4 inwards towards face 2
Step 4: Fold face 5 downwards towards face 2
Step 5: Fold face 6 inwards towards face 3
Based on the above steps, can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "1-3-2 Net", "faces": {"6": [[0.9999999999999999, 1.0, 0.0], [1.0, 2.0, 0.0], [1.0, 2.0, 1.0], [0.9999999999999999, 1.0, 1.0]], "2": [[1.0, 2.0, 0.0], [2.0, 2.0, 0.0], [2.0, 2.0, 1.0], [1.0, 2.0, 1.0]], "3": [[1, 1, 0], [2, 1, 0], [2, 2, 0], [1, 2, 0]], "1": [[1.0, 0.9999999999999999, 1.0], [2.0, 0.9999999999999999, 1.0], [2.0, 1.0, 0.0], [1.0, 1.0, 0.0]], "4": [[2.0, 0.9999999999999999, 1.0], [2.0, 2.0, 1.0], [2.0, 2.0, 1.1102230246251565e-16], [2.0, 1.0, 0.0]], "5": [[1.0, 0.9999999999999998, 1.0], [1.0, 1.9999999999999998, 1.0], [2.0, 2.0, 1.0], [2.0, 0.9999999999999999, 1.0]]}, "face_connections": {"6": ["2"], "2": ["6", "3"], "3": ["2", "1"], "1": ["3", "4"], "4": ["1", "5"], "5": ["4"]}, "valid": true}, "base_face": "3", "folding_steps": [["1", "3", [1, 1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["2", "3", [2, 2, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["4", "1", [2.0, 0.9999999999999999, 1.0], [0.0, 1.1102230246251565e-16, -1.0], -1.5707963267948966], ["5", "4", [2.0, 0.9999999999999999, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["6", "2", [1.0, 2.0, 0.0], [0.0, 0.0, 1.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 2 upwards", "Fold face 4 inwards towards face 2", "Fold face 5 downwards towards face 2", "Fold face 6 inwards towards face 3"], "images_per_step": ["output_dir/folding_nets/random3_net9_base3_step1.png", "output_dir/folding_nets/random3_net9_base3_step2.png", "output_dir/folding_nets/random3_net9_base3_step3.png", "output_dir/folding_nets/random3_net9_base3_step4.png", "output_dir/folding_nets/random3_net9_base3_step5.png", "output_dir/folding_nets/random3_net9_base3_step6.png"], "id": "random3_net9_base3"} | q+steps | [
"yes",
"no"
] |
|
296_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "Big T Net", "faces": {"4": [[3.0, 0.0, 1.0000000000000002], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [3.0, 1.0, 1.0000000000000002]], "3": [[2.0, 0.0, 1.0], [2.0, 0.0, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, 1.0]], "5": [[2, 0, 0], [3, 0, 0], [3, 1, 0], [2, 1, 0]], "1": [[3.0, -6.123233995736766e-17, 1.0], [3.0, -6.123233995736766e-17, 0.0], [2.0, 0.0, 0.0], [2.0, 0.0, 1.0]], "6": [[3.0, 0.9999999999999999, 1.0], [3.0, 0.9999999999999999, 0.0], [3.0, -6.123233995736766e-17, 0.0], [3.0, -6.123233995736766e-17, 1.0]], "2": [[2.0, 1.0000000000000004, 1.0], [2.0, 1.0000000000000004, 0.0], [3.0, 0.9999999999999999, 0.0], [3.0, 0.9999999999999999, 1.0]]}, "face_connections": {"4": ["3"], "3": ["4", "5", "1"], "5": ["3"], "1": ["3", "6"], "6": ["1", "2"], "2": ["6"]}, "valid": true}, "base_face": "5", "folding_steps": [["3", "5", [2, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["1", "3", [2.0, 0.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["4", "3", [2.0, 0.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["6", "1", [3.0, -6.123233995736766e-17, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["2", "6", [3.0, 0.9999999999999999, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 3 upwards", "Fold face 1 inwards towards face 5", "Fold face 4 downwards towards face 1", "Fold face 6 inwards towards face 4", "Fold face 2 inwards towards face 4"], "images_per_step": ["output_dir/folding_nets/random3_net3_base5_step1.png", "output_dir/folding_nets/random3_net3_base5_step2.png", "output_dir/folding_nets/random3_net3_base5_step3.png", "output_dir/folding_nets/random3_net3_base5_step4.png", "output_dir/folding_nets/random3_net3_base5_step5.png", "output_dir/folding_nets/random3_net3_base5_step6.png"], "id": "random3_net3_base5"} | q_only | [
"yes",
"no"
] |
|
234_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 6 as the base:
Step 1: Fold face 5 upwards
Step 2: Fold face 1 upwards
Step 3: Fold face 3 inwards towards face 6
Step 4: Fold face 4 downwards towards face 1
Step 5: Fold face 2 downwards towards face 1
Based on the above steps, can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "3-3 Net", "faces": {"2": [[2.0, -0.9999999999999999, 1.0], [2.0, 1.1442377452219642e-17, 1.0], [2.0000000000000004, -3.8347585052928364e-17, 0.0], [2.0000000000000004, -0.9999999999999999, 0.0]], "4": [[0.9999999999999999, -0.9999999999999999, 1.0], [1.0, 6.123233995736765e-17, 1.0], [2.0, 1.1442377452219642e-17, 1.0], [2.0, -0.9999999999999999, 1.0]], "3": [[0.9999999999999999, -1.0, 6.123233995736766e-17], [1.0, 0.0, 0.0], [1.0, 6.123233995736765e-17, 1.0], [0.9999999999999999, -0.9999999999999999, 1.0]], "1": [[1.0, 0.0, 0.0], [2.0, 0.0, 0.0], [2.0, 6.123233995736766e-17, 1.0], [1.0, 6.123233995736766e-17, 1.0]], "6": [[1, -1, 0], [2, -1, 0], [2, 0, 0], [1, 0, 0]], "5": [[1.0, -1.0, 1.0], [2.0, -1.0, 1.0], [2.0, -1.0, 0.0], [1.0, -1.0, 0.0]]}, "face_connections": {"2": ["4"], "4": ["2", "3"], "3": ["4", "1"], "1": ["3", "6"], "6": ["1", "5"], "5": ["6"]}, "valid": true}, "base_face": "6", "folding_steps": [["5", "6", [1, -1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["1", "6", [2, 0, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["3", "1", [1.0, 0.0, 0.0], [0.0, 6.123233995736766e-17, 1.0], 1.5707963267948966], ["4", "3", [1.0, 6.123233995736765e-17, 1.0], [-1.1102230246251565e-16, -1.0, 0.0], -1.5707963267948966], ["2", "4", [2.0, 1.1442377452219642e-17, 1.0], [0.0, -1.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 5 upwards", "Fold face 1 upwards", "Fold face 3 inwards towards face 6", "Fold face 4 downwards towards face 1", "Fold face 2 downwards towards face 1"], "images_per_step": ["output_dir/folding_nets/random1_net7_base6_step1.png", "output_dir/folding_nets/random1_net7_base6_step2.png", "output_dir/folding_nets/random1_net7_base6_step3.png", "output_dir/folding_nets/random1_net7_base6_step4.png", "output_dir/folding_nets/random1_net7_base6_step5.png", "output_dir/folding_nets/random1_net7_base6_step6.png"], "id": "random1_net7_base6"} | q+steps | [
"yes",
"no"
] |
|
382_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 6 as the base:
Step 1: Fold face 3 upwards
Step 2: Fold face 1 downwards
Step 3: Fold face 5 downwards towards face 3
Step 4: Fold face 4 downwards towards face 6
Step 5: Fold face 2 upwards towards face 3
Based on the above steps, can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=2)", "faces": {"2": [[4.0, 1.0, -9.494107596574928e-16], [5.0, 1.0, 0.0], [5.0, 2.0, 0.0], [4.0, 2.0, -9.494107596574928e-16]], "4": [[5.0, 1.0, 0.0], [5.0, 1.0, 1.0], [5.0, 2.0, 1.0], [5.0, 2.0, 0.0]], "1": [[5.0, 1.0, 1.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [5.0, 2.0, 1.0]], "3": [[4.0, 1.0, 1.0], [4.0, 1.0, 0.0], [4.0, 2.0, 0.0], [4.0, 2.0, 1.0]], "6": [[4, 1, 0], [5, 1, 0], [5, 2, 0], [4, 2, 0]], "5": [[5.0, 0.9999999999999999, 0.0], [4.0, 0.9999999999999999, 0.0], [4.0, 1.0, 1.0], [5.0, 1.0, 1.0]]}, "face_connections": {"2": ["4"], "4": ["2", "1"], "1": ["4", "3", "5"], "3": ["1", "6"], "6": ["3"], "5": ["1"]}, "valid": false}, "base_face": "6", "folding_steps": [["3", "6", [4, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["1", "3", [4.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["5", "1", [5.0, 1.0, 1.0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["4", "1", [5.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "4", [5.0, 1.0, 0.0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 3 upwards", "Fold face 1 downwards", "Fold face 5 downwards towards face 3", "Fold face 4 downwards towards face 6", "Fold face 2 upwards towards face 3"], "images_per_step": ["output_dir/folding_nets/random1_net15_base6_step1.png", "output_dir/folding_nets/random1_net15_base6_step2.png", "output_dir/folding_nets/random1_net15_base6_step3.png", "output_dir/folding_nets/random1_net15_base6_step4.png"], "id": "random1_net15_base6"} | q+steps | [
"no",
"yes"
] |
|
343_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 1 as the base:
Step 1: Fold face 6 upwards
Step 2: Fold face 2 upwards towards face 6
Step 3: Fold face 3 downwards towards face 6
Step 4: Fold face 4 downwards towards face 1
Step 5: Fold face 5 upwards towards face 1
Based on the above steps, can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=0)", "faces": {"1": [[0, 1, 0], [1, 1, 0], [1, 2, 0], [0, 2, 0]], "2": [[1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [1.0, 2.0, 1.0], [1.0, 2.0, 0.0]], "3": [[1.0, 1.0, 1.0], [0.0, 1.0, 1.0000000000000002], [0.0, 2.0, 1.0000000000000002], [1.0, 2.0, 1.0]], "4": [[0.0, 1.0, 1.0000000000000002], [-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [-2.83276944882399e-16, 2.0, 2.220446049250313e-16], [0.0, 2.0, 1.0000000000000002]], "5": [[-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [0.9999999999999997, 1.0, 9.957992501029596e-17], [0.9999999999999997, 2.0, 9.957992501029596e-17], [-2.83276944882399e-16, 2.0, 2.220446049250313e-16]], "6": [[0.0, 0.9999999999999999, 1.0], [1.0, 0.9999999999999999, 1.0], [1.0, 1.0, 0.0], [0.0, 1.0, 0.0]]}, "face_connections": {"1": ["2", "6"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4"], "6": ["1"]}, "valid": false}, "base_face": "1", "folding_steps": [["6", "1", [0, 1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["2", "1", [1, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["3", "2", [1.0, 1.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "3", [0.0, 1.0, 1.0000000000000002], [0.0, 1.0, 0.0], -1.5707963267948966], ["5", "4", [-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [0.0, 1.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 2 upwards towards face 6", "Fold face 3 downwards towards face 6", "Fold face 4 downwards towards face 1", "Fold face 5 upwards towards face 1"], "images_per_step": ["output_dir/folding_nets/net13_base1_step1.png", "output_dir/folding_nets/net13_base1_step2.png", "output_dir/folding_nets/net13_base1_step3.png", "output_dir/folding_nets/net13_base1_step4.png"], "id": "net13_base1"} | q+steps | [
"no",
"yes"
] |
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