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qid stringlengths 8 32	question stringlengths 94 436	answer stringclasses 2 values	question_info stringlengths 1.35k 2.1k	type stringclasses 5 values	choices sequencelengths 2 2
16_q+steps+all_intermediate_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 3 as the base: Step 1: Fold face 4 upwards <image_1> Step 2: Fold face 2 upwards <image_2> Step 3: Fold face 5 downwards towards face 2 <image_3> Step 4: Fold face 6 upwards towards face 2 <image_4> 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": {"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, 0.0], [1.0, 1.0, 1.0], [0.0, 1.0, 1.0], [0.0, 1.0, 0.0]]}, "face_connections": {"1": ["4"], "2": ["3"], "3": ["2", "4", "6"], "4": ["1", "3", "5"], "5": ["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", "4", [1.0, 1.0, 1.0], [0.0, 0.0, -1.0], -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 inwards towards face 3"], "images_per_step": ["output_dir/folding_nets/net1_base3_step1.png", "output_dir/folding_nets/net1_base3_step2.png", "output_dir/folding_nets/net1_base3_step3.png", "output_dir/folding_nets/net1_base3_step4.png", "output_dir/folding_nets/net1_base3_step5.png", "output_dir/folding_nets/net1_base3_step6.png"], "id": "net1_base3"}	q+steps+all_intermediate_vis	[ "no", "yes" ]
98_q+steps+partial_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 4 as the base: Step 1: Fold face 2 upwards <image_1> Step 2: Fold face 5 upwards <image_2> Step 3: Fold face 3 inwards towards face 2 <image_3> Step 4: Fold face 6 downwards towards face 2 <image_4> 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?	B	{"initial_net": {"name": "Big T - Variant 2", "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, -1.0, 1.0], [2.0, 0.0, 1.0], [2.0, 0.0, 0.0], [2.0, -1.0, 0.0]], "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", "4"], "3": ["5"], "4": ["2", "5"], "5": ["4", "3", "6"], "6": ["5"]}, "valid": true}, "base_face": "4", "folding_steps": [["2", "4", [2, 0, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["5", "4", [1, -1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["3", "5", [2.0, -1.0, 1.0], [0.0, 0.0, -1.0], -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 5 upwards", "Fold face 3 inwards towards face 2", "Fold face 6 downwards towards face 2", "Fold face 1 inwards towards face 4"], "images_per_step": ["output_dir/folding_nets/net5_base4_step1.png", "output_dir/folding_nets/net5_base4_step2.png", "output_dir/folding_nets/net5_base4_step3.png", "output_dir/folding_nets/net5_base4_step4.png", "output_dir/folding_nets/net5_base4_step5.png", "output_dir/folding_nets/net5_base4_step6.png"], "id": "net5_base4"}	q+steps+partial_vis	[ "no", "yes" ]
100_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": {"1": [[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]], "4": [[1.0, 0.9999999999999999, 1.0], [2.0, 0.9999999999999999, 1.0], [2.0, 1.0, 0.0], [1.0, 1.0, 0.0]], "5": [[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]], "6": [[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": {"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", [2, 2, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["4", "3", [1, 1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["5", "4", [2.0, 0.9999999999999999, 1.0], [0.0, 1.1102230246251565e-16, -1.0], -1.5707963267948966], ["6", "5", [2.0, 0.9999999999999999, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["1", "2", [1.0, 2.0, 0.0], [0.0, 0.0, 1.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 4 upwards", "Fold face 5 inwards towards face 2", "Fold face 6 downwards towards face 2", "Fold face 1 inwards towards face 3"], "images_per_step": ["output_dir/folding_nets/net9_base3_step1.png", "output_dir/folding_nets/net9_base3_step2.png", "output_dir/folding_nets/net9_base3_step3.png", "output_dir/folding_nets/net9_base3_step4.png", "output_dir/folding_nets/net9_base3_step5.png", "output_dir/folding_nets/net9_base3_step6.png"], "id": "net9_base3"}	q_only	[ "yes", "no" ]
140_q+steps+partial_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 1 as the base: Step 1: Fold face 4 upwards <image_1> Step 2: Fold face 3 inwards towards face 1 <image_2> Step 3: Fold face 2 inwards towards face 1 <image_3> Step 4: Fold face 5 downwards towards face 2 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": "1-3-2 Net", "faces": {"1": [[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0]], "2": [[0.0, 1.0, 0.0], [0.0, 1.0, 1.0], [-2.83276944882399e-16, 0.0, 1.0], [-2.83276944882399e-16, 0.0, 0.0]], "3": [[1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [0.0, 1.0, 1.0], [0.0, 1.0, 0.0]], "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": [[0.9999999999999998, -6.123233995736766e-17, 0.0], [-2.220446049250313e-16, -6.123233995736767e-17, 2.220446049250313e-16], [0.0, 0.0, 1.0000000000000002], [1.0, 0.0, 1.0]]}, "face_connections": {"1": ["4"], "2": ["3"], "3": ["2", "4"], "4": ["1", "3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": true}, "base_face": "1", "folding_steps": [["4", "1", [1, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["3", "4", [1.0, 1.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["2", "3", [0.0, 1.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["5", "4", [1.0, 0.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["6", "5", [1.0, 0.0, 1.0], [-1.0, 0.0, 2.220446049250313e-16], -1.5707963267948966]], "folding_step_descs": ["Fold face 4 upwards", "Fold face 3 inwards towards face 1", "Fold face 2 inwards towards face 1", "Fold face 5 downwards towards face 2", "Fold face 6 downwards towards face 1"], "images_per_step": ["output_dir/folding_nets/net11_base1_step1.png", "output_dir/folding_nets/net11_base1_step2.png", "output_dir/folding_nets/net11_base1_step3.png", "output_dir/folding_nets/net11_base1_step4.png", "output_dir/folding_nets/net11_base1_step5.png", "output_dir/folding_nets/net11_base1_step6.png"], "id": "net11_base1"}	q+steps+partial_vis	[ "no", "yes" ]
87_q+steps+partial_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 4 as the base: Step 1: Fold face 3 upwards <image_1> Step 2: Fold face 2 downwards <image_2> 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?	A	{"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+partial_vis	[ "no", "yes" ]
134_q+steps+partial_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 2 as the base: Step 1: Fold face 1 upwards <image_1> Step 2: Fold face 3 upwards Step 3: Fold face 4 downwards towards face 1 Step 4: Fold face 5 downwards towards face 1 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": "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+steps+partial_vis	[ "no", "yes" ]
137_q+steps+all_intermediate_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 2 as the base: Step 1: Fold face 1 upwards <image_1> Step 2: Fold face 3 upwards <image_2> Step 4: Fold face 5 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": "Net B: Row 5 + Face 6 (shift=4)", "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": [[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": {"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", [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", "5", [1.0, 1.0, 1.0], [-3.3306690738754696e-16, 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 downwards towards face 1"], "images_per_step": ["output_dir/folding_nets/net17_base2_step1.png", "output_dir/folding_nets/net17_base2_step2.png", "output_dir/folding_nets/net17_base2_step3.png"], "id": "net17_base2"}	q+steps+all_intermediate_vis	[ "no", "yes" ]
45_q+steps+all_intermediate_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 5 as the base: Step 1: Fold face 4 upwards <image_1> Step 2: Fold face 3 downwards <image_2> Step 3: Fold face 2 downwards towards face 5 <image_3> Step 4: Fold face 6 downwards towards face 2 <image_4> 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": {"3": [[3.0, 0.0, 1.0000000000000002], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [3.0, 1.0, 1.0000000000000002]], "1": [[3.0, 1.0, 1.0000000000000002], [2.0, 1.0, 1.0], [2.0, 1.0, 0.0], [3.0, 1.0, 2.220446049250313e-16]], "2": [[3.0000000000000004, 0.0, 2.220446049250313e-16], [3.0, 0.0, 1.0000000000000002], [3.0, 1.0, 1.0000000000000002], [3.0000000000000004, 1.0, 2.220446049250313e-16]], "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": [[3.0, -6.123233995736766e-17, 2.220446049250313e-16], [2.0, -6.123233995736767e-17, 0.0], [2.0, 0.0, 1.0], [3.0, 0.0, 1.0000000000000002]]}, "face_connections": {"1": ["3"], "2": ["3"], "3": ["1", "2", "4", "6"], "4": ["3", "5"], "5": ["4"], "6": ["3"]}, "valid": true}, "base_face": "5", "folding_steps": [["4", "5", [2, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "4", [2.0, 0.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "3", [3.0, 0.0, 1.0000000000000002], [0.0, 1.0, 0.0], 1.5707963267948966], ["6", "3", [3.0, 0.0, 1.0000000000000002], [-1.0, 0.0, -2.220446049250313e-16], -1.5707963267948966], ["1", "3", [2.0, 1.0, 1.0], [1.0, 0.0, 2.220446049250313e-16], -1.5707963267948966]], "folding_step_descs": ["Fold face 4 upwards", "Fold face 3 downwards", "Fold face 2 downwards towards face 5", "Fold face 6 downwards towards face 2", "Fold face 1 downwards towards face 2"], "images_per_step": ["output_dir/folding_nets/net0_base5_step1.png", "output_dir/folding_nets/net0_base5_step2.png", "output_dir/folding_nets/net0_base5_step3.png", "output_dir/folding_nets/net0_base5_step4.png", "output_dir/folding_nets/net0_base5_step5.png", "output_dir/folding_nets/net0_base5_step6.png"], "id": "net0_base5"}	q+steps+all_intermediate_vis	[ "yes", "no" ]
26_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" ]
80_q+steps+all_intermediate_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 2 as the base: Step 1: Fold face 1 upwards <image_1> Step 2: Fold face 4 upwards towards face 1 <image_2> Step 4: Fold face 5 inwards towards face 2 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": "Net H: Two rows with bottom row shifted right", "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": [[1.0, 0.9999999999999999, 1.0], [2.0, 0.9999999999999999, 1.0], [2.0, 1.0, 0.0], [1.0, 1.0, 0.0]], "5": [[1.9999999999999998, 2.0, 6.123233995736766e-17], [1.9999999999999998, 2.0, 1.0], [2.0, 1.0, 1.0], [2.0, 1.0, 0.0]], "6": [[1.9999999999999998, 2.0, 1.0], [0.9999999999999998, 1.9999999999999998, 1.0], [1.0, 0.9999999999999998, 1.0], [2.0, 1.0, 1.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3", "4"], "3": ["2", "5"], "4": ["2", "5"], "5": ["3", "4", "6"], "6": ["5"]}, "valid": false}, "base_face": "2", "folding_steps": [["1", "2", [1, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["4", "2", [1, 1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["3", "2", [2, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["5", "3", [2.0, 1.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["6", "5", [1.9999999999999998, 2.0, 1.0], [2.220446049250313e-16, -1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 4 upwards towards face 1", "Fold face 3 upwards towards face 4", "Fold face 5 inwards towards face 2", "Fold face 6 downwards towards face 1"], "images_per_step": ["output_dir/folding_nets/net23_base2_step1.png", "output_dir/folding_nets/net23_base2_step2.png", "output_dir/folding_nets/net23_base2_step3.png"], "id": "net23_base2"}	q+steps+all_intermediate_vis	[ "yes", "no" ]
115_q+steps+partial_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 5 as the base: Step 1: Fold face 4 upwards <image_1> Step 2: Fold face 3 downwards <image_2> Step 3: Fold face 2 downwards towards face 5 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": "t-shaped Net Variant 1", "faces": {"3": [[3.0, 0.0, 1.0000000000000002], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [3.0, 1.0, 1.0000000000000002]], "2": [[3.0000000000000004, 0.0, 2.220446049250313e-16], [3.0, 0.0, 1.0000000000000002], [3.0, 1.0, 1.0000000000000002], [3.0000000000000004, 1.0, 2.220446049250313e-16]], "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": [[3.0, -6.123233995736766e-17, 2.220446049250313e-16], [2.0, -6.123233995736767e-17, 0.0], [2.0, 0.0, 1.0], [3.0, 0.0, 1.0000000000000002]], "1": [[2.0, 1.0, 1.0], [2.0, 1.0, 0.0], [3.0, 1.0, 0.0], [3.0, 1.0, 1.0]]}, "face_connections": {"1": ["4"], "2": ["3"], "3": ["2", "4", "6"], "4": ["1", "3", "5"], "5": ["4"], "6": ["3"]}, "valid": true}, "base_face": "5", "folding_steps": [["4", "5", [2, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "4", [2.0, 0.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "3", [3.0, 0.0, 1.0000000000000002], [0.0, 1.0, 0.0], 1.5707963267948966], ["6", "3", [3.0, 0.0, 1.0000000000000002], [-1.0, 0.0, -2.220446049250313e-16], -1.5707963267948966], ["1", "4", [2.0, 1.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 4 upwards", "Fold face 3 downwards", "Fold face 2 downwards towards face 5", "Fold face 6 downwards towards face 2", "Fold face 1 inwards towards face 3"], "images_per_step": ["output_dir/folding_nets/net1_base5_step1.png", "output_dir/folding_nets/net1_base5_step2.png", "output_dir/folding_nets/net1_base5_step3.png", "output_dir/folding_nets/net1_base5_step4.png", "output_dir/folding_nets/net1_base5_step5.png", "output_dir/folding_nets/net1_base5_step6.png"], "id": "net1_base5"}	q+steps+partial_vis	[ "no", "yes" ]
43_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 1 upwards Step 2: Fold face 3 upwards Step 3: Fold face 4 inwards towards face 1 Step 4: Fold face 5 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": "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+steps	[ "yes", "no" ]
35_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 inwards towards face 1 Step 3: Fold face 3 inwards towards face 1 Step 4: Fold face 2 inwards towards face 5 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": "t-shaped Net Variant 2", "faces": {"3": [[3.0, 2.0000000000000004, 1.0000000000000002], [2.0, 2.0, 1.0], [2.0, 2.0, 1.1102230246251565e-16], [3.0, 2.0000000000000004, 2.220446049250313e-16]], "2": [[3.0, 1.0000000000000004, 1.0000000000000004], [3.0, 2.0000000000000004, 1.0000000000000002], [3.0, 2.0000000000000004, 2.220446049250313e-16], [3.0, 1.0000000000000004, 3.3306690738754696e-16]], "4": [[2.0, 2.0, 1.0], [2.0, 0.9999999999999999, 1.0], [2.0, 1.0, 0.0], [2.0, 2.0, 1.1102230246251565e-16]], "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]], "6": [[3.0000000000000004, 1.0000000000000007, 0.9999999999999999], [2.0000000000000004, 1.0, 1.0], [2.0, 2.0, 1.0], [3.0, 2.0000000000000004, 1.0000000000000002]], "1": [[2, 1, 0], [3, 1, 0], [3, 2, 0], [2, 2, 0]]}, "face_connections": {"1": ["5"], "2": ["3"], "3": ["2", "4", "6"], "4": ["3", "5"], "5": ["1", "4"], "6": ["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, 0.9999999999999999, 1.0], [0.0, 1.1102230246251565e-16, -1.0], 1.5707963267948966], ["3", "4", [2.0, 2.0, 1.0], [0.0, 0.0, -1.0], 1.5707963267948966], ["2", "3", [3.0, 2.0000000000000004, 1.0000000000000002], [0.0, 0.0, -1.0], 1.5707963267948966], ["6", "3", [3.0, 2.0000000000000004, 1.0000000000000002], [-1.0, -4.440892098500626e-16, -2.220446049250313e-16], -1.5707963267948966]], "folding_step_descs": ["Fold face 5 upwards", "Fold face 4 inwards towards face 1", "Fold face 3 inwards towards face 1", "Fold face 2 inwards towards face 5", "Fold face 6 downwards towards face 2"], "images_per_step": ["output_dir/folding_nets/net2_base1_step1.png", "output_dir/folding_nets/net2_base1_step2.png", "output_dir/folding_nets/net2_base1_step3.png", "output_dir/folding_nets/net2_base1_step4.png", "output_dir/folding_nets/net2_base1_step5.png", "output_dir/folding_nets/net2_base1_step6.png"], "id": "net2_base1"}	q+steps	[ "no", "yes" ]
12_q+steps+all_intermediate_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 1 as the base: Step 1: Fold face 2 upwards <image_1> Step 2: Fold face 3 inwards towards face 1 <image_2> Step 3: Fold face 4 downwards towards face 2 <image_3> 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?	A	{"initial_net": {"name": "Invalid D", "faces": {"1": [[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0]], "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": [[1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [1.0, 0.0, 1.0], [1.0, 0.0, 0.0]], "4": [[1.0, 1.0, 1.0], [1.0, 0.0, 1.0], [0.0, 0.0, 1.0000000000000002], [0.0, 1.0, 1.0000000000000002]], "5": [[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]], "6": [[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": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": false}, "base_face": "1", "folding_steps": [["2", "1", [1, 1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["3", "2", [1.0, 1.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["4", "3", [1.0, 1.0, 1.0], [0.0, -1.0, 0.0], 1.5707963267948966], ["5", "4", [1.0, 0.0, 1.0], [-1.0, 0.0, 2.220446049250313e-16], -1.5707963267948966], ["6", "5", [0.9999999999999998, -2.83276944882399e-16, 0.0], [-1.0, 0.0, 2.220446049250313e-16], -1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 3 inwards towards face 1", "Fold face 4 downwards towards face 2", "Fold face 5 downwards towards face 1", "Fold face 6 upwards towards face 1"], "images_per_step": ["output_dir/folding_nets/net19_base1_step1.png", "output_dir/folding_nets/net19_base1_step2.png", "output_dir/folding_nets/net19_base1_step3.png", "output_dir/folding_nets/net19_base1_step4.png"], "id": "net19_base1"}	q+steps+all_intermediate_vis	[ "no", "yes" ]
111_q+steps+all_intermediate_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 1 as the base: Step 1: Fold face 3 upwards <image_1> Step 2: Fold face 4 inwards towards face 1 <image_2> Step 3: Fold face 2 inwards towards face 1 <image_3> Step 4: Fold face 5 downwards towards face 2 <image_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": {"1": [[0, 1, 0], [1, 1, 0], [1, 2, 0], [0, 2, 0]], "2": [[1.0, 2.0, 0.0], [1.0, 2.0, 1.0], [0.0, 2.0, 1.0], [0.0, 2.0, 0.0]], "3": [[1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [1.0, 2.0, 1.0], [1.0, 2.0, 0.0]], "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": [[0.0, 0.9999999999999999, 1.0], [-1.1102230246251568e-16, 2.0, 1.0000000000000002], [0.9999999999999999, 2.0, 1.0000000000000002], [1.0, 1.0, 1.0]], "6": [[4.978996250514797e-17, 1.0, 0.0], [-1.7225464241988333e-16, 2.0, 3.3306690738754696e-16], [-1.1102230246251565e-16, 2.0, 1.0000000000000002], [0.0, 0.9999999999999999, 1.0]]}, "face_connections": {"1": ["3"], "2": ["3"], "3": ["1", "2", "4"], "4": ["3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": true}, "base_face": "1", "folding_steps": [["3", "1", [1, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "3", [1.0, 1.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["2", "3", [1.0, 2.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["5", "4", [0.0, 0.9999999999999999, 1.0], [1.0, 1.1102230246251565e-16, 0.0], -1.5707963267948966], ["6", "5", [0.0, 0.9999999999999999, 1.0], [-1.1102230246251568e-16, 1.0, 2.220446049250313e-16], -1.5707963267948966]], "folding_step_descs": ["Fold face 3 upwards", "Fold face 4 inwards towards face 1", "Fold face 2 inwards towards face 1", "Fold face 5 downwards towards face 2", "Fold face 6 downwards towards face 1"], "images_per_step": ["output_dir/folding_nets/net10_base1_step1.png", "output_dir/folding_nets/net10_base1_step2.png", "output_dir/folding_nets/net10_base1_step3.png", "output_dir/folding_nets/net10_base1_step4.png", "output_dir/folding_nets/net10_base1_step5.png", "output_dir/folding_nets/net10_base1_step6.png"], "id": "net10_base1"}	q+steps+all_intermediate_vis	[ "no", "yes" ]
110_q+steps+all_for_valid_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 6 as the base: Step 1: Fold face 5 upwards <image_1> Step 2: Fold face 4 inwards towards face 6 <image_2> Step 3: Fold face 3 downwards towards face 5 <image_3> Step 4: Fold face 2 downwards towards face 5 <image_4> Step 5: Fold face 1 downwards towards face 2 <image_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": {"1": [[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]], "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": ["4"], "2": ["3"], "3": ["2", "4"], "4": ["1", "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", "4", [2.0, -1.0, 6.123233995736766e-17], [0.0, 1.1102230246251568e-16, 1.0], 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/net11_base6_step1.png", "output_dir/folding_nets/net11_base6_step2.png", "output_dir/folding_nets/net11_base6_step3.png", "output_dir/folding_nets/net11_base6_step4.png", "output_dir/folding_nets/net11_base6_step5.png", "output_dir/folding_nets/net11_base6_step6.png"], "id": "net11_base6"}	q+steps+all_for_valid_vis	[ "no", "yes" ]
57_q+steps+all_for_valid_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 3 as the base: Step 1: Fold face 2 upwards <image_1> Step 2: Fold face 4 inwards towards face 3 <image_2> Step 3: Fold face 5 inwards towards face 3 <image_3> Step 4: Fold face 6 inwards towards face 2 <image_4> Step 5: Fold face 1 downwards towards face 4 <image_5> 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": {"1": [[3.0, 0.0, 1.0000000000000002], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [3.0, 1.0, 1.0000000000000002]], "2": [[2.0, 0.0, 1.0], [2.0, 0.0, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, 1.0]], "3": [[2, 0, 0], [3, 0, 0], [3, 1, 0], [2, 1, 0]], "4": [[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]], "5": [[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]], "6": [[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": {"1": ["2"], "2": ["1", "3", "4"], "3": ["2"], "4": ["2", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": true}, "base_face": "3", "folding_steps": [["2", "3", [2, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["4", "2", [2.0, 0.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["5", "4", [3.0, -6.123233995736766e-17, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["6", "5", [3.0, 0.9999999999999999, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["1", "2", [2.0, 0.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 4 inwards towards face 3", "Fold face 5 inwards towards face 3", "Fold face 6 inwards towards face 2", "Fold face 1 downwards towards face 4"], "images_per_step": ["output_dir/folding_nets/net3_base3_step1.png", "output_dir/folding_nets/net3_base3_step2.png", "output_dir/folding_nets/net3_base3_step3.png", "output_dir/folding_nets/net3_base3_step4.png", "output_dir/folding_nets/net3_base3_step5.png", "output_dir/folding_nets/net3_base3_step6.png"], "id": "net3_base3"}	q+steps+all_for_valid_vis	[ "no", "yes" ]
63_q+steps+all_intermediate_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 1 as the base: Step 1: Fold face 2 upwards <image_1> Step 2: Fold face 4 inwards towards face 1 <image_2> Step 3: Fold face 5 inwards towards face 1 <image_3> Step 4: Fold face 6 inwards towards face 1 <image_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 3", "faces": {"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]], "3": [[0.9999999999999999, 1.0, 1.0], [1.0, 0.0, 1.0000000000000002], [0.0, 0.0, 1.0000000000000002], [-1.1102230246251565e-16, 0.9999999999999999, 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]], "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]], "6": [[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": {"1": ["2"], "2": ["1", "4"], "3": ["6"], "4": ["2", "5"], "5": ["4", "6"], "6": ["5", "3"]}, "valid": true}, "base_face": "1", "folding_steps": [["2", "1", [1, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "2", [1.0, 0.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["5", "4", [0.0, -6.123233995736766e-17, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["6", "5", [-1.2246467991473532e-16, 0.9999999999999999, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["3", "6", [0.9999999999999999, 1.0, 1.0], [-1.0, -1.1102230246251565e-16, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 4 inwards towards face 1", "Fold face 5 inwards towards face 1", "Fold face 6 inwards towards face 1", "Fold face 3 downwards towards face 2"], "images_per_step": ["output_dir/folding_nets/net6_base1_step1.png", "output_dir/folding_nets/net6_base1_step2.png", "output_dir/folding_nets/net6_base1_step3.png", "output_dir/folding_nets/net6_base1_step4.png", "output_dir/folding_nets/net6_base1_step5.png", "output_dir/folding_nets/net6_base1_step6.png"], "id": "net6_base1"}	q+steps+all_intermediate_vis	[ "no", "yes" ]
88_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" ]
58_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 Step 3: Fold face 5 downwards towards face 1 Step 4: Fold face 6 downwards 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?	A	{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=4)", "faces": {"1": [[3.0, 1.0, 1.0000000000000002], [2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [3.0, 2.0, 1.0000000000000002]], "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]], "3": [[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]], "6": [[3.0, 0.9999999999999999, 0.0], [2.0, 0.9999999999999999, 0.0], [2.0, 1.0, 1.0], [3.0, 1.0, 1.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": false}, "base_face": "3", "folding_steps": [["2", "3", [2, 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], ["6", "5", [3.0, 1.0, 1.0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["1", "2", [2.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 4 upwards", "Fold face 5 downwards towards face 1", "Fold face 6 downwards towards face 2", "Fold face 1 downwards towards face 4"], "images_per_step": ["output_dir/folding_nets/net17_base3_step1.png", "output_dir/folding_nets/net17_base3_step2.png", "output_dir/folding_nets/net17_base3_step3.png"], "id": "net17_base3"}	q+steps	[ "no", "yes" ]
74_q+steps+all_intermediate_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 5 as the base: Step 1: Fold face 4 upwards <image_1> Step 2: Fold face 3 downwards <image_2> Step 3: Fold face 2 downwards towards face 5 <image_3> 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?	B	{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=2)", "faces": {"1": [[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]], "2": [[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]], "4": [[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]], "6": [[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": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4", "6"], "4": ["3", "5"], "5": ["4"], "6": ["3"]}, "valid": false}, "base_face": "5", "folding_steps": [["4", "5", [4, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "4", [4.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "3", [5.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["6", "3", [5.0, 1.0, 1.0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["1", "2", [5.0, 1.0, 0.0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 4 upwards", "Fold face 3 downwards", "Fold face 2 downwards towards face 5", "Fold face 6 downwards towards face 2", "Fold face 1 upwards towards face 4"], "images_per_step": ["output_dir/folding_nets/net15_base5_step1.png", "output_dir/folding_nets/net15_base5_step2.png", "output_dir/folding_nets/net15_base5_step3.png", "output_dir/folding_nets/net15_base5_step4.png"], "id": "net15_base5"}	q+steps+all_intermediate_vis	[ "yes", "no" ]
83_q+steps+all_intermediate_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 6 as the base: Step 1: Fold face 3 upwards <image_1> Step 2: Fold face 5 upwards towards face 3 <image_2> Step 3: Fold face 4 downwards towards face 3 <image_3> Step 4: Fold face 2 downwards towards face 3 <image_4> 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": {"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, 0.0], [2.0, -3.0, 1.0], [2.0, -2.0, 1.0], [2.0, -2.0, 0.0]], "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": ["6"], "4": ["2", "5"], "5": ["4", "6"], "6": ["5", "3"]}, "valid": true}, "base_face": "6", "folding_steps": [["3", "6", [2, -3, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["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], ["1", "2", [1.0, -3.0, 1.0000000000000002], [0.0, -4.440892098500626e-16, -1.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 3 upwards", "Fold face 5 upwards towards face 3", "Fold face 4 downwards towards face 3", "Fold face 2 downwards towards face 3", "Fold face 1 downwards towards face 4"], "images_per_step": ["output_dir/folding_nets/net6_base6_step1.png", "output_dir/folding_nets/net6_base6_step2.png", "output_dir/folding_nets/net6_base6_step3.png", "output_dir/folding_nets/net6_base6_step4.png", "output_dir/folding_nets/net6_base6_step5.png", "output_dir/folding_nets/net6_base6_step6.png"], "id": "net6_base6"}	q+steps+all_intermediate_vis	[ "yes", "no" ]
95_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 inwards towards face 1 Step 3: Fold face 2 inwards towards face 1 Step 4: Fold face 5 inwards 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?	B	{"initial_net": {"name": "t-shaped Net", "faces": {"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]], "1": [[0, 1, 0], [1, 1, 0], [1, 2, 0], [0, 2, 0]], "2": [[-6.123233995736766e-17, 2.0, 1.0], [0.0, 0.9999999999999999, 1.0], [0.0, 1.0, 0.0], [-6.123233995736766e-17, 2.0, 1.1102230246251565e-16]], "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": [[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]], "6": [[0.0, 2.0, 1.0], [1.0, 2.0, 1.0], [1.0, 0.9999999999999999, 1.0], [0.0, 0.9999999999999999, 1.0]]}, "face_connections": {"1": ["3"], "2": ["3"], "3": ["1", "2", "4", "6"], "4": ["3", "5"], "5": ["4"], "6": ["3"]}, "valid": true}, "base_face": "1", "folding_steps": [["3", "1", [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], ["2", "3", [0.0, 0.9999999999999999, 1.0], [0.0, 1.1102230246251565e-16, -1.0], 1.5707963267948966], ["5", "4", [1.0, 2.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["6", "3", [0.0, 0.9999999999999999, 1.0], [1.0, 0.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 3 upwards", "Fold face 4 inwards towards face 1", "Fold face 2 inwards towards face 1", "Fold face 5 inwards towards face 1", "Fold face 6 downwards towards face 2"], "images_per_step": ["output_dir/folding_nets/net0_base1_step1.png", "output_dir/folding_nets/net0_base1_step2.png", "output_dir/folding_nets/net0_base1_step3.png", "output_dir/folding_nets/net0_base1_step4.png", "output_dir/folding_nets/net0_base1_step5.png", "output_dir/folding_nets/net0_base1_step6.png"], "id": "net0_base1"}	q+steps	[ "no", "yes" ]
91_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 downwards towards face 6 Step 4: Fold face 2 downwards towards face 5 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": "invalid_G", "faces": {"2": [[4.0, 0.0, 0.0], [4.0, 0.0, 1.0], [4.0, 1.0, 1.0], [4.0, 1.0, 0.0]], "3": [[4.0, 0.0, 1.0], [3.0, 0.0, 1.0], [3.0, 1.0, 1.0], [4.0, 1.0, 1.0]], "4": [[3.0, 0.0, 1.0], [3.0, 0.0, 0.0], [3.0, 1.0, 0.0], [3.0, 1.0, 1.0]], "5": [[3, 0, 0], [4, 0, 0], [4, 1, 0], [3, 1, 0]], "1": [[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": {"2": ["3", "1"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4", "6"], "1": ["2"], "6": ["5"]}, "valid": false}, "base_face": "5", "folding_steps": [["6", "5", [4, 1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["4", "5", [3, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "4", [3.0, 0.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "3", [4.0, 0.0, 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]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 4 upwards towards face 6", "Fold face 3 downwards towards face 6", "Fold face 2 downwards towards face 5", "Fold face 1 inwards towards face 3"], "images_per_step": ["output_dir/folding_nets/net20_base5_step1.png", "output_dir/folding_nets/net20_base5_step2.png", "output_dir/folding_nets/net20_base5_step3.png", "output_dir/folding_nets/net20_base5_step4.png"], "id": "net20_base5"}	q+steps	[ "yes", "no" ]
20_q+steps+all_intermediate_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 2 as the base: Step 1: Fold face 1 upwards <image_1> Step 2: Fold face 4 upwards towards face 1 <image_2> Step 3: Fold face 3 upwards towards face 4 <image_3> Step 4: Fold face 5 downwards towards face 1 <image_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, 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]], "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]], "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]], "5": [[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": ["2"], "2": ["1", "3", "4"], "3": ["2"], "4": ["2", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": true}, "base_face": "2", "folding_steps": [["1", "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", "2", [2, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["5", "4", [1.0, -6.123233995736766e-17, 1.0], [1.0, 0.0, 0.0], -1.5707963267948966], ["6", "5", [1.0, 0.9999999999999999, 1.0000000000000002], [1.0, 0.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 4 upwards towards face 1", "Fold face 3 upwards towards face 4", "Fold face 5 downwards towards face 1", "Fold face 6 downwards towards face 1"], "images_per_step": ["output_dir/folding_nets/net3_base2_step1.png", "output_dir/folding_nets/net3_base2_step2.png", "output_dir/folding_nets/net3_base2_step3.png", "output_dir/folding_nets/net3_base2_step4.png", "output_dir/folding_nets/net3_base2_step5.png", "output_dir/folding_nets/net3_base2_step6.png"], "id": "net3_base2"}	q+steps+all_intermediate_vis	[ "yes", "no" ]
60_q+steps+all_intermediate_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 1 as the base: Step 1: Fold face 2 upwards <image_1> Step 3: Fold face 3 inwards Step 4: Fold face 5 downwards Step 5: Fold face 6 downwards 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": {"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+steps+all_intermediate_vis	[ "no", "yes" ]
11_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 2 inwards towards face 6 Step 3: Fold face 4 inwards towards face 6 Step 4: Fold face 5 inwards towards face 1 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?	B	{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=2)", "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]], "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]], "4": [[3.0, 1.0, 0.0], [3.0, 0.0, 0.0], [3.0, 0.0, 1.0], [3.0, 1.0, 1.0]], "5": [[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]], "6": [[2, 0, 0], [3, 0, 0], [3, 1, 0], [2, 1, 0]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4", "6"], "4": ["3", "5"], "5": ["4"], "6": ["3"]}, "valid": false}, "base_face": "6", "folding_steps": [["3", "6", [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], ["4", "3", [3.0, 1.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["5", "4", [3.0, 0.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["1", "2", [2.0, 0.0, 0.0], [0.0, 0.0, 1.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 3 upwards", "Fold face 2 inwards towards face 6", "Fold face 4 inwards towards face 6", "Fold face 5 inwards towards face 1", "Fold face 1 inwards towards face 4"], "images_per_step": ["output_dir/folding_nets/net15_base6_step1.png", "output_dir/folding_nets/net15_base6_step2.png", "output_dir/folding_nets/net15_base6_step3.png", "output_dir/folding_nets/net15_base6_step4.png"], "id": "net15_base6"}	q+steps	[ "yes", "no" ]
3_q+steps+all_intermediate_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 3 as the base: Step 1: Fold face 5 upwards <image_1> Step 2: Fold face 4 inwards towards face 3 <image_2> Step 3: Fold face 2 inwards towards face 3 <image_3> Step 4: Fold face 6 inwards towards face 2 <image_4> 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]], "2": [[3.0, -0.9999999999999999, 1.0], [3.0, -0.9999999999999999, 0.0], [3.0, -2.0, 0.0], [3.0, -2.0, 1.0]], "3": [[2, -2, 0], [3, -2, 0], [3, -1, 0], [2, -1, 0]], "4": [[2.0, -1.0, 1.0], [2.0, -1.0, 0.0], [3.0, -0.9999999999999999, 0.0], [3.0, -0.9999999999999999, 1.0]], "5": [[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": ["2"], "2": ["1", "4"], "3": ["5"], "4": ["2", "5"], "5": ["4", "3", "6"], "6": ["5"]}, "valid": true}, "base_face": "3", "folding_steps": [["5", "3", [2, -2, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["4", "5", [2.0, -1.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["2", "4", [3.0, -0.9999999999999999, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["6", "5", [2.0, -2.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["1", "2", [3.0, -0.9999999999999999, 1.0], [0.0, -1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 5 upwards", "Fold face 4 inwards towards face 3", "Fold face 2 inwards towards face 3", "Fold face 6 inwards towards face 2", "Fold face 1 downwards towards face 4"], "images_per_step": ["output_dir/folding_nets/net5_base3_step1.png", "output_dir/folding_nets/net5_base3_step2.png", "output_dir/folding_nets/net5_base3_step3.png", "output_dir/folding_nets/net5_base3_step4.png", "output_dir/folding_nets/net5_base3_step5.png", "output_dir/folding_nets/net5_base3_step6.png"], "id": "net5_base3"}	q+steps+all_intermediate_vis	[ "yes", "no" ]
118_q+steps+partial_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 4 as the base: Step 1: Fold face 2 upwards <image_1> Step 2: Fold face 5 upwards <image_2> Step 3: Fold face 6 downwards towards face 2 Step 4: Fold face 3 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 - Variant 3", "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, 1.0000000000000002], [2.0, 2.220446049250313e-16, 2.220446049250313e-16], [2.0, -0.9999999999999998, 0.0], [2.0, -1.0, 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", "4"], "3": ["6"], "4": ["2", "5"], "5": ["4", "6"], "6": ["5", "3"]}, "valid": true}, "base_face": "4", "folding_steps": [["2", "4", [2, 0, 0], [-1.0, 0.0, 0.0], -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], ["3", "6", [2.0, 0.0, 1.0000000000000002], [0.0, -1.0, -2.220446049250313e-16], -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 5 upwards", "Fold face 6 downwards towards face 2", "Fold face 3 downwards towards face 2", "Fold face 1 inwards towards face 4"], "images_per_step": ["output_dir/folding_nets/net6_base4_step1.png", "output_dir/folding_nets/net6_base4_step2.png", "output_dir/folding_nets/net6_base4_step3.png", "output_dir/folding_nets/net6_base4_step4.png", "output_dir/folding_nets/net6_base4_step5.png", "output_dir/folding_nets/net6_base4_step6.png"], "id": "net6_base4"}	q+steps+partial_vis	[ "yes", "no" ]
71_q+steps+partial_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 6 as the base: Step 1: Fold face 5 upwards <image_1> Step 2: Fold face 4 inwards towards face 6 <image_2> 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+partial_vis	[ "no", "yes" ]
67_q+steps+all_intermediate_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 2 as the base: Step 1: Fold face 1 upwards <image_1> Step 2: Fold face 4 upwards towards face 1 <image_2> Step 3: Fold face 5 downwards towards face 1 <image_3> Step 4: Fold face 6 downwards towards face 1 <image_4> 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": {"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]], "2": [[1, 0, 0], [2, 0, 0], [2, 1, 0], [1, 1, 0]], "3": [[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]], "5": [[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": ["2"], "2": ["1", "4"], "3": ["6"], "4": ["2", "5"], "5": ["4", "6"], "6": ["5", "3"]}, "valid": true}, "base_face": "2", "folding_steps": [["1", "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], ["5", "4", [1.0, -6.123233995736766e-17, 1.0], [1.0, 0.0, 0.0], -1.5707963267948966], ["6", "5", [1.0, 0.9999999999999999, 1.0000000000000002], [1.0, 0.0, 0.0], -1.5707963267948966], ["3", "6", [2.0, 1.0, 2.220446049250313e-16], [0.0, -1.1102230246251565e-16, 1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 4 upwards towards face 1", "Fold face 5 downwards towards face 1", "Fold face 6 downwards towards face 1", "Fold face 3 inwards towards face 2"], "images_per_step": ["output_dir/folding_nets/net6_base2_step1.png", "output_dir/folding_nets/net6_base2_step2.png", "output_dir/folding_nets/net6_base2_step3.png", "output_dir/folding_nets/net6_base2_step4.png", "output_dir/folding_nets/net6_base2_step5.png", "output_dir/folding_nets/net6_base2_step6.png"], "id": "net6_base2"}	q+steps+all_intermediate_vis	[ "yes", "no" ]
23_q+steps+partial_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 6 as the base: Step 1: Fold face 5 upwards <image_1> Step 2: Fold face 4 inwards towards face 6 <image_2> 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 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, -1.0, 0.9999999999999997], [3.0, -0.9999999999999999, 1.0], [3.0000000000000004, -0.9999999999999998, 0.0], [2.0000000000000004, -0.9999999999999999, -4.440892098500626e-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": ["2"], "2": ["1", "3"], "3": ["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", "2", [3.0, -0.9999999999999999, 1.0], [4.440892098500626e-16, 1.1102230246251565e-16, -1.0], 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 3"], "images_per_step": ["output_dir/folding_nets/net9_base6_step1.png", "output_dir/folding_nets/net9_base6_step2.png", "output_dir/folding_nets/net9_base6_step3.png", "output_dir/folding_nets/net9_base6_step4.png", "output_dir/folding_nets/net9_base6_step5.png", "output_dir/folding_nets/net9_base6_step6.png"], "id": "net9_base6"}	q+steps+partial_vis	[ "no", "yes" ]
47_q+steps+all_intermediate_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 6 as the base: Step 1: Fold face 3 upwards <image_1> Step 2: Fold face 2 inwards towards face 6 <image_2> Step 3: Fold face 4 inwards towards face 6 <image_3> Step 4: Fold face 5 downwards towards face 2 <image_4> 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": {"3": [[0.0, 0.0, 0.0], [1.0, 0.0, 0.0], [1.0, 6.123233995736766e-17, 1.0], [0.0, 6.123233995736766e-17, 1.0]], "2": [[-6.123233995736766e-17, -1.0, 6.123233995736766e-17], [0.0, 0.0, 0.0], [0.0, 6.123233995736765e-17, 1.0], [-6.123233995736766e-17, -0.9999999999999999, 1.0]], "4": [[1.0, 0.0, 0.0], [1.0, -1.0, 6.123233995736766e-17], [1.0, -0.9999999999999999, 1.0], [1.0, 6.123233995736765e-17, 1.0]], "5": [[1.0, -1.0, 6.123233995736766e-17], [0.0, -1.0000000000000002, 1.1442377452219691e-17], [-2.220446049250313e-16, -1.0000000000000002, 1.0000000000000002], [1.0, -0.9999999999999999, 1.0]], "6": [[0, -1, 0], [1, -1, 0], [1, 0, 0], [0, 0, 0]], "1": [[1.0, -0.9999999999999999, 1.0], [-2.220446049250313e-16, -1.0000000000000002, 1.0000000000000002], [-5.551115123125781e-16, -4.440892098500626e-16, 1.0], [0.9999999999999992, 0.0, 1.0]]}, "face_connections": {"1": ["5"], "2": ["3"], "3": ["2", "4", "6"], "4": ["3", "5"], "5": ["1", "4"], "6": ["3"]}, "valid": true}, "base_face": "6", "folding_steps": [["3", "6", [1, 0, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["2", "3", [0.0, 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], ["5", "4", [1.0, -1.0, 6.123233995736766e-17], [0.0, 1.1102230246251568e-16, 1.0], -1.5707963267948966], ["1", "5", [-2.220446049250313e-16, -1.0000000000000002, 1.0000000000000002], [1.0, 3.330669073875469e-16, -2.2204460492503126e-16], -1.5707963267948966]], "folding_step_descs": ["Fold face 3 upwards", "Fold face 2 inwards towards face 6", "Fold face 4 inwards towards face 6", "Fold face 5 downwards towards face 2", "Fold face 1 downwards towards face 3"], "images_per_step": ["output_dir/folding_nets/net2_base6_step1.png", "output_dir/folding_nets/net2_base6_step2.png", "output_dir/folding_nets/net2_base6_step3.png", "output_dir/folding_nets/net2_base6_step4.png", "output_dir/folding_nets/net2_base6_step5.png", "output_dir/folding_nets/net2_base6_step6.png"], "id": "net2_base6"}	q+steps+all_intermediate_vis	[ "yes", "no" ]
66_q+steps+all_intermediate_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 5 as the base: Step 1: Fold face 4 upwards <image_1> Step 2: Fold face 3 downwards <image_2> Step 3: Fold face 2 downwards towards face 5 <image_3> Step 4: Fold face 6 downwards towards face 2 <image_4> 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": [[3.0, 0.0, 1.0000000000000002], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [3.0, 1.0, 1.0000000000000002]], "2": [[3.0000000000000004, 0.0, 2.220446049250313e-16], [3.0, 0.0, 1.0000000000000002], [3.0, 1.0, 1.0000000000000002], [3.0000000000000004, 1.0, 2.220446049250313e-16]], "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": [[3.0, -6.123233995736766e-17, 2.220446049250313e-16], [2.0, -6.123233995736767e-17, 0.0], [2.0, 0.0, 1.0], [3.0, 0.0, 1.0000000000000002]], "1": [[2.0, 1.0, 0.0], [3.0, 1.0, 0.0], [3.0, 1.0, 1.0], [2.0, 1.0, 1.0]]}, "face_connections": {"1": ["5"], "2": ["3"], "3": ["2", "4", "6"], "4": ["3", "5"], "5": ["1", "4"], "6": ["3"]}, "valid": true}, "base_face": "5", "folding_steps": [["4", "5", [2, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "4", [2.0, 0.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "3", [3.0, 0.0, 1.0000000000000002], [0.0, 1.0, 0.0], 1.5707963267948966], ["6", "3", [3.0, 0.0, 1.0000000000000002], [-1.0, 0.0, -2.220446049250313e-16], -1.5707963267948966], ["1", "5", [3, 1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 4 upwards", "Fold face 3 downwards", "Fold face 2 downwards towards face 5", "Fold face 6 downwards towards face 2", "Fold face 1 upwards towards face 3"], "images_per_step": ["output_dir/folding_nets/net2_base5_step1.png", "output_dir/folding_nets/net2_base5_step2.png", "output_dir/folding_nets/net2_base5_step3.png", "output_dir/folding_nets/net2_base5_step4.png", "output_dir/folding_nets/net2_base5_step5.png", "output_dir/folding_nets/net2_base5_step6.png"], "id": "net2_base5"}	q+steps+all_intermediate_vis	[ "no", "yes" ]
114_q+steps+all_intermediate_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 1 as the base: Step 1: Fold face 2 upwards <image_1> Step 3: Fold face 3 upwards towards face 1 Step 4: Fold face 5 upwards 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?	B	{"initial_net": {"name": "2 Rows of 3", "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, 2.0, 6.123233995736766e-17], [1.0000000000000002, 3.0, 1.2246467991473535e-16], [1.1102230246251565e-16, 3.0, 6.123233995736767e-17], [0.0, 2.0, 0.0]], "4": [[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": [[1.0000000000000002, 0.9999999999999998, 0.9999999999999998], [0.9999999999999999, 1.9999999999999998, 1.0], [0.9999999999999999, 2.0, 3.749399456654644e-33], [1.0000000000000002, 1.0, -2.220446049250313e-16]], "6": [[0.9999999999999999, 1.9999999999999998, 1.0], [-3.3306690738754696e-16, 1.9999999999999998, 1.0000000000000002], [-1.1102230246251565e-16, 2.0, 0.0], [0.9999999999999999, 2.0, 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": "1", "folding_steps": [["2", "1", [1, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "1", [0, 1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["3", "2", [1.0, 2.0, 6.123233995736766e-17], [2.220446049250313e-16, 1.0, 6.123233995736766e-17], 1.5707963267948966], ["5", "2", [1.0, 1.0, 0.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["6", "5", [0.9999999999999999, 1.9999999999999998, 1.0], [0.0, 2.220446049250313e-16, -1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 4 upwards towards face 2", "Fold face 3 upwards towards face 1", "Fold face 5 upwards towards face 1", "Fold face 6 downwards towards face 1"], "images_per_step": ["output_dir/folding_nets/net18_base1_step1.png", "output_dir/folding_nets/net18_base1_step2.png"], "id": "net18_base1"}	q+steps+all_intermediate_vis	[ "yes", "no" ]
49_q+steps+all_intermediate_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 5 as the base: Step 1: Fold face 6 upwards <image_1> Step 2: Fold face 4 upwards <image_2> Step 3: Fold face 3 inwards towards face 5 <image_3> 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": "Invalid D", "faces": {"1": [[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]], "3": [[3.0, 2.0, 1.0], [2.0, 2.0, 1.0], [2.0, 2.0, 0.0], [3.0, 2.0, 0.0]], "4": [[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": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": false}, "base_face": "5", "folding_steps": [["6", "5", [3, 2, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "5", [2, 2, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "4", [2.0, 2.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["2", "3", [3.0, 2.0, 1.0], [-1.0, 0.0, 0.0], 1.5707963267948966], ["1", "2", [3.0, 3.0, 1.0000000000000002], [0.0, -1.0, -2.220446049250313e-16], -1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 4 upwards", "Fold face 3 inwards towards face 5", "Fold face 2 downwards towards face 4", "Fold face 1 downwards towards face 3"], "images_per_step": ["output_dir/folding_nets/net19_base5_step1.png", "output_dir/folding_nets/net19_base5_step2.png", "output_dir/folding_nets/net19_base5_step3.png", "output_dir/folding_nets/net19_base5_step4.png"], "id": "net19_base5"}	q+steps+all_intermediate_vis	[ "yes", "no" ]
40_q+steps+all_intermediate_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 3 as the base: Step 1: Fold face 2 upwards <image_1> Step 2: Fold face 4 upwards towards face 2 <image_2> Step 3: Fold face 5 inwards towards face 3 <image_3> Step 4: Fold face 6 downwards towards face 2 <image_4> 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+all_intermediate_vis	[ "no", "yes" ]
13_q+steps+all_for_valid_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 6 as the base: Step 1: Fold face 5 upwards <image_1> Step 2: Fold face 4 downwards <image_2> Step 3: Fold face 2 downwards towards face 6 <image_3> Step 4: Fold face 3 downwards towards face 4 <image_4> Step 5: Fold face 1 downwards towards face 4 <image_5> 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, -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+steps+all_for_valid_vis	[ "yes", "no" ]
34_q+steps+all_intermediate_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 5 as the base: Step 1: Fold face 4 upwards <image_1> Step 2: Fold face 3 downwards <image_2> Step 3: Fold face 2 downwards towards face 5 <image_3> 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": "Net B: Row 5 + Face 6 (shift=3)", "faces": {"1": [[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]], "2": [[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]], "4": [[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]], "6": [[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": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5", "6"], "5": ["4"], "6": ["4"]}, "valid": false}, "base_face": "5", "folding_steps": [["4", "5", [4, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "4", [4.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "3", [5.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["6", "4", [4.0, 1.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["1", "2", [5.0, 1.0, 0.0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 4 upwards", "Fold face 3 downwards", "Fold face 2 downwards towards face 5", "Fold face 6 inwards towards face 2", "Fold face 1 upwards towards face 4"], "images_per_step": ["output_dir/folding_nets/net16_base5_step1.png", "output_dir/folding_nets/net16_base5_step2.png", "output_dir/folding_nets/net16_base5_step3.png", "output_dir/folding_nets/net16_base5_step4.png"], "id": "net16_base5"}	q+steps+all_intermediate_vis	[ "no", "yes" ]
84_q+steps+all_intermediate_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 2 as the base: Step 1: Fold face 1 upwards <image_1> Step 2: Fold face 4 upwards towards face 1 <image_2> Step 3: Fold face 5 downwards towards face 1 <image_3> Step 4: Fold face 3 downwards towards face 2 <image_4> 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": [[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]], "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]], "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]], "5": [[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": ["2"], "2": ["1", "4"], "3": ["5"], "4": ["2", "5"], "5": ["4", "3", "6"], "6": ["5"]}, "valid": true}, "base_face": "2", "folding_steps": [["1", "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], ["5", "4", [1.0, -6.123233995736766e-17, 1.0], [1.0, 0.0, 0.0], -1.5707963267948966], ["3", "5", [2.0, 0.9999999999999999, 1.0000000000000002], [0.0, -1.0, -2.220446049250313e-16], -1.5707963267948966], ["6", "5", [1.0, 0.9999999999999999, 1.0000000000000002], [1.0, 0.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 4 upwards towards face 1", "Fold face 5 downwards towards face 1", "Fold face 3 downwards towards face 2", "Fold face 6 downwards towards face 1"], "images_per_step": ["output_dir/folding_nets/net5_base2_step1.png", "output_dir/folding_nets/net5_base2_step2.png", "output_dir/folding_nets/net5_base2_step3.png", "output_dir/folding_nets/net5_base2_step4.png", "output_dir/folding_nets/net5_base2_step5.png", "output_dir/folding_nets/net5_base2_step6.png"], "id": "net5_base2"}	q+steps+all_intermediate_vis	[ "yes", "no" ]
15_q+steps+partial_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 2 as the base: Step 1: Fold face 1 upwards <image_1> Step 2: Fold face 3 upwards Step 3: Fold face 4 downwards towards face 1 Step 4: Fold face 5 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?	B	{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=3)", "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": [[2.0, 0.9999999999999999, 0.0], [1.0, 0.9999999999999999, 0.0], [1.0, 1.0, 1.0], [2.0, 1.0, 1.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5", "6"], "5": ["4"], "6": ["4"]}, "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", "4", [2.0, 1.0, 1.0], [-1.0, 0.0, 0.0], -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 downwards towards face 1"], "images_per_step": ["output_dir/folding_nets/net16_base2_step1.png", "output_dir/folding_nets/net16_base2_step2.png", "output_dir/folding_nets/net16_base2_step3.png"], "id": "net16_base2"}	q+steps+partial_vis	[ "yes", "no" ]
81_q+steps+partial_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 3 as the base: Step 1: Fold face 2 upwards <image_1> Step 2: Fold face 4 upwards Step 3: Fold face 5 upwards towards face 2 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": "invalid_F", "faces": {"1": [[3.0, 1.0, 1.0000000000000002], [2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [3.0, 2.0, 1.0000000000000002]], "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]], "3": [[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": [[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, 1.0, 1.0], [2.0, 1.0, 1.0], [2.0, 1.0, 6.123233995736766e-17], [3.0, 1.0, 0.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4", "5"], "4": ["3", "6"], "5": ["3", "6"], "6": ["4", "5"]}, "valid": false}, "base_face": "3", "folding_steps": [["2", "3", [2, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["4", "3", [3, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["5", "3", [2, 1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["6", "4", [3.0, 1.0, 0.0], [0.0, 0.0, 1.0], 1.5707963267948966], ["1", "2", [2.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 4 upwards", "Fold face 5 upwards towards face 2", "Fold face 6 inwards towards face 2", "Fold face 1 downwards towards face 4"], "images_per_step": ["output_dir/folding_nets/net21_base3_step1.png", "output_dir/folding_nets/net21_base3_step2.png", "output_dir/folding_nets/net21_base3_step3.png", "output_dir/folding_nets/net21_base3_step4.png"], "id": "net21_base3"}	q+steps+partial_vis	[ "yes", "no" ]
132_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 inwards towards face 2 Step 4: Fold face 6 upwards 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": "invalid_F", "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, 0.9999999999999999, 1.0], [4.0, 0.9999999999999999, 0.0], [3.0, 1.0, 0.0], [3.0, 1.0, 1.0]], "6": [[3.0, 0.9999999999999999, 1.0], [4.0, 0.9999999999999998, 0.9999999999999999], [4.0, 0.9999999999999999, -1.1102230246251565e-16], [3.0, 1.0, 0.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4", "5"], "4": ["3", "6"], "5": ["3", "6"], "6": ["4", "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", "3", [3.0, 1.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["6", "5", [4.0, 0.9999999999999999, 0.0], [-1.0, 1.1102230246251565e-16, 0.0], 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 inwards towards face 2", "Fold face 6 upwards towards face 2", "Fold face 1 downwards towards face 4"], "images_per_step": ["output_dir/folding_nets/net21_base4_step1.png", "output_dir/folding_nets/net21_base4_step2.png", "output_dir/folding_nets/net21_base4_step3.png"], "id": "net21_base4"}	q+steps	[ "yes", "no" ]
126_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 downwards Step 3: Fold face 4 downwards towards face 1 Step 4: Fold face 5 inwards 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?	A	{"initial_net": {"name": "invalid_F", "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, 0.0, 2.0], [4.930380657631324e-32, 1.3596310734468924e-32, 1.0000000000000002], [1.0, 6.123233995736769e-17, 1.0], [1.0000000000000002, 6.123233995736766e-17, 1.9999999999999998]], "6": [[4.930380657631324e-32, 1.3596310734468924e-32, 1.0000000000000002], [-1.2246467991473537e-16, 1.0, 1.0000000000000002], [0.9999999999999999, 1.0, 0.9999999999999999], [1.0, 6.123233995736769e-17, 1.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4", "5"], "4": ["3", "6"], "5": ["3", "6"], "6": ["4", "5"]}, "valid": false}, "base_face": "1", "folding_steps": [["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", "3", [2.83276944882399e-16, 0.0, 2.0], [-2.8327694488239903e-16, 0.0, -1.0], 1.5707963267948966], ["6", "5", [4.930380657631324e-32, 1.3596310734468924e-32, 1.0000000000000002], [1.0, 6.123233995736767e-17, -2.220446049250313e-16], 1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 3 downwards", "Fold face 4 downwards towards face 1", "Fold face 5 inwards", "Fold face 6 upwards towards face 3"], "images_per_step": ["output_dir/folding_nets/net21_base1_step1.png", "output_dir/folding_nets/net21_base1_step2.png", "output_dir/folding_nets/net21_base1_step3.png"], "id": "net21_base1"}	q+steps	[ "no", "yes" ]
115_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 4 upwards Step 2: Fold face 3 downwards Step 3: Fold face 2 downwards towards face 5 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?	A	{"initial_net": {"name": "t-shaped Net Variant 1", "faces": {"3": [[3.0, 0.0, 1.0000000000000002], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [3.0, 1.0, 1.0000000000000002]], "2": [[3.0000000000000004, 0.0, 2.220446049250313e-16], [3.0, 0.0, 1.0000000000000002], [3.0, 1.0, 1.0000000000000002], [3.0000000000000004, 1.0, 2.220446049250313e-16]], "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": [[3.0, -6.123233995736766e-17, 2.220446049250313e-16], [2.0, -6.123233995736767e-17, 0.0], [2.0, 0.0, 1.0], [3.0, 0.0, 1.0000000000000002]], "1": [[2.0, 1.0, 1.0], [2.0, 1.0, 0.0], [3.0, 1.0, 0.0], [3.0, 1.0, 1.0]]}, "face_connections": {"1": ["4"], "2": ["3"], "3": ["2", "4", "6"], "4": ["1", "3", "5"], "5": ["4"], "6": ["3"]}, "valid": true}, "base_face": "5", "folding_steps": [["4", "5", [2, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "4", [2.0, 0.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "3", [3.0, 0.0, 1.0000000000000002], [0.0, 1.0, 0.0], 1.5707963267948966], ["6", "3", [3.0, 0.0, 1.0000000000000002], [-1.0, 0.0, -2.220446049250313e-16], -1.5707963267948966], ["1", "4", [2.0, 1.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 4 upwards", "Fold face 3 downwards", "Fold face 2 downwards towards face 5", "Fold face 6 downwards towards face 2", "Fold face 1 inwards towards face 3"], "images_per_step": ["output_dir/folding_nets/net1_base5_step1.png", "output_dir/folding_nets/net1_base5_step2.png", "output_dir/folding_nets/net1_base5_step3.png", "output_dir/folding_nets/net1_base5_step4.png", "output_dir/folding_nets/net1_base5_step5.png", "output_dir/folding_nets/net1_base5_step6.png"], "id": "net1_base5"}	q+steps	[ "yes", "no" ]
92_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 inwards towards face 4 Step 3: Fold face 5 upwards towards face 3 Step 4: Fold face 6 inwards 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": "2-2 net", "faces": {"1": [[0.9999999999999999, 1.0, 1.0], [1.0, 2.0, 1.0], [2.0, 2.0, 1.0], [2.0, 1.0, 1.0]], "2": [[0.9999999999999999, 1.0, 0.0], [1.0, 2.0, 0.0], [1.0, 2.0, 1.0], [0.9999999999999999, 1.0, 1.0]], "3": [[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, 1, 0], [2, 1, 0], [2, 2, 0], [1, 2, 0]], "5": [[2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [2.0, 2.0, 0.0]], "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"], "4": ["3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": true}, "base_face": "4", "folding_steps": [["3", "4", [2, 2, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["2", "3", [1.0, 2.0, 0.0], [0.0, 0.0, 1.0], 1.5707963267948966], ["5", "4", [2, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["6", "5", [2.0, 1.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["1", "2", [1.0, 2.0, 1.0], [-1.1102230246251565e-16, -1.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 3 upwards", "Fold face 2 inwards towards face 4", "Fold face 5 upwards towards face 3", "Fold face 6 inwards towards face 2", "Fold face 1 downwards towards face 3"], "images_per_step": ["output_dir/folding_nets/net8_base4_step1.png", "output_dir/folding_nets/net8_base4_step2.png", "output_dir/folding_nets/net8_base4_step3.png", "output_dir/folding_nets/net8_base4_step4.png", "output_dir/folding_nets/net8_base4_step5.png", "output_dir/folding_nets/net8_base4_step6.png"], "id": "net8_base4"}	q+steps	[ "no", "yes" ]
25_q+steps+all_intermediate_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 4 as the base: Step 1: Fold face 3 upwards <image_1> Step 2: Fold face 2 downwards <image_2> Step 4: Fold face 6 downwards towards face 1 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": "Linear 6-Face Row", "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]], "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]], "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]], "4": [[3, 0, 0], [4, 0, 0], [4, 1, 0], [3, 1, 0]], "5": [[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": {"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, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "3", [3.0, 0.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["5", "4", [4, 0, 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], ["1", "2", [4.0, 0.0, 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 downwards towards face 1", "Fold face 1 downwards towards face 4"], "images_per_step": ["output_dir/folding_nets/net12_base4_step1.png", "output_dir/folding_nets/net12_base4_step2.png", "output_dir/folding_nets/net12_base4_step3.png"], "id": "net12_base4"}	q+steps+all_intermediate_vis	[ "yes", "no" ]
68_q+steps+all_for_valid_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 3 as the base: Step 1: Fold face 6 upwards <image_1> Step 2: Fold face 5 inwards towards face 3 <image_2> Step 3: Fold face 4 inwards towards face 3 <image_3> Step 4: Fold face 2 inwards towards face 3 <image_4> Step 5: Fold face 1 downwards towards face 4 <image_5> 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": {"1": [[3.0000000000000004, -2.0, 1.0], [3.0000000000000004, -3.0, 1.0], [2.0000000000000004, -3.0, 1.0], [2.0000000000000004, -2.0, 1.0]], "2": [[3.0000000000000004, -3.0, 1.0], [3.0000000000000004, -3.0, 0.0], [2.0000000000000004, -3.0, 0.0], [2.0000000000000004, -3.0, 1.0]], "3": [[2, -3, 0], [3, -3, 0], [3, -2, 0], [2, -2, 0]], "4": [[3.0, -2.0, 1.0], [3.0, -2.0, 0.0], [3.0000000000000004, -3.0, 0.0], [3.0000000000000004, -3.0, 1.0]], "5": [[2.0, -2.0, 1.0], [2.0, -2.0, 0.0], [3.0, -2.0, 0.0], [3.0, -2.0, 1.0]], "6": [[2.0, -3.0, 1.0], [2.0, -3.0, 0.0], [2.0, -2.0, 0.0], [2.0, -2.0, 1.0]]}, "face_connections": {"1": ["2"], "2": ["1", "4"], "3": ["6"], "4": ["2", "5"], "5": ["4", "6"], "6": ["5", "3"]}, "valid": true}, "base_face": "3", "folding_steps": [["6", "3", [2, -3, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["5", "6", [2.0, -2.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["4", "5", [3.0, -2.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["2", "4", [3.0000000000000004, -3.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["1", "2", [3.0000000000000004, -3.0, 1.0], [-1.0, 0.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 5 inwards towards face 3", "Fold face 4 inwards towards face 3", "Fold face 2 inwards towards face 3", "Fold face 1 downwards towards face 4"], "images_per_step": ["output_dir/folding_nets/net6_base3_step1.png", "output_dir/folding_nets/net6_base3_step2.png", "output_dir/folding_nets/net6_base3_step3.png", "output_dir/folding_nets/net6_base3_step4.png", "output_dir/folding_nets/net6_base3_step5.png", "output_dir/folding_nets/net6_base3_step6.png"], "id": "net6_base3"}	q+steps+all_for_valid_vis	[ "no", "yes" ]
84_q+steps+all_for_valid_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 2 as the base: Step 1: Fold face 1 upwards <image_1> Step 2: Fold face 4 upwards towards face 1 <image_2> Step 3: Fold face 5 downwards towards face 1 <image_3> Step 4: Fold face 3 downwards towards face 2 <image_4> Step 5: Fold face 6 downwards towards face 1 <image_5> 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": [[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]], "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]], "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]], "5": [[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": ["2"], "2": ["1", "4"], "3": ["5"], "4": ["2", "5"], "5": ["4", "3", "6"], "6": ["5"]}, "valid": true}, "base_face": "2", "folding_steps": [["1", "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], ["5", "4", [1.0, -6.123233995736766e-17, 1.0], [1.0, 0.0, 0.0], -1.5707963267948966], ["3", "5", [2.0, 0.9999999999999999, 1.0000000000000002], [0.0, -1.0, -2.220446049250313e-16], -1.5707963267948966], ["6", "5", [1.0, 0.9999999999999999, 1.0000000000000002], [1.0, 0.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 4 upwards towards face 1", "Fold face 5 downwards towards face 1", "Fold face 3 downwards towards face 2", "Fold face 6 downwards towards face 1"], "images_per_step": ["output_dir/folding_nets/net5_base2_step1.png", "output_dir/folding_nets/net5_base2_step2.png", "output_dir/folding_nets/net5_base2_step3.png", "output_dir/folding_nets/net5_base2_step4.png", "output_dir/folding_nets/net5_base2_step5.png", "output_dir/folding_nets/net5_base2_step6.png"], "id": "net5_base2"}	q+steps+all_for_valid_vis	[ "yes", "no" ]
31_q+steps+partial_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 2 as the base: Step 1: Fold face 1 upwards <image_1> Step 2: Fold face 3 upwards Step 3: Fold face 4 downwards towards face 1 Step 4: Fold face 5 downwards 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?	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]], "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": [[3.0, 0.0, 0.9999999999999999], [2.0, 0.0, 1.0], [2.0, 6.123233995736766e-17, 0.0], [3.0, 6.123233995736766e-17, -1.1102230246251565e-16]], "6": [[2.0, 0.0, 1.0], [1.9999999999999998, 1.0, 1.0], [1.9999999999999998, 1.0, 2.220446049250313e-16], [2.0, 6.123233995736765e-17, 0.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4", "5"], "4": ["3", "6"], "5": ["3", "6"], "6": ["4", "5"]}, "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", "3", [3.0, 0.0, 0.9999999999999999], [-1.0, 0.0, 1.1102230246251565e-16], 1.5707963267948966], ["6", "5", [2.0, 0.0, 1.0], [0.0, 6.123233995736766e-17, -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", "Fold face 6 inwards towards face 3"], "images_per_step": ["output_dir/folding_nets/net21_base2_step1.png", "output_dir/folding_nets/net21_base2_step2.png", "output_dir/folding_nets/net21_base2_step3.png"], "id": "net21_base2"}	q+steps+partial_vis	[ "yes", "no" ]
62_q+steps+partial_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 2 as the base: Step 1: Fold face 1 upwards <image_1> Step 2: Fold face 3 upwards Step 3: Fold face 4 downwards towards face 1 Step 4: Fold face 5 downwards 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?	B	{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=0)", "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": [[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]]}, "face_connections": {"1": ["2", "6"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4"], "6": ["1"]}, "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", "1", [0.9999999999999999, 1.0, 1.0], [1.1102230246251565e-16, 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 2"], "images_per_step": ["output_dir/folding_nets/net13_base2_step1.png", "output_dir/folding_nets/net13_base2_step2.png", "output_dir/folding_nets/net13_base2_step3.png", "output_dir/folding_nets/net13_base2_step4.png"], "id": "net13_base2"}	q+steps+partial_vis	[ "yes", "no" ]
112_q+steps+all_intermediate_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 1 as the base: Step 1: Fold face 2 upwards <image_1> Step 2: Fold face 3 downwards <image_2> Step 3: Fold face 4 downwards towards face 1 <image_3> Step 4: Fold face 5 inwards towards face 1 <image_4> 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": [[0, 2, 0], [1, 2, 0], [1, 3, 0], [0, 3, 0]], "2": [[0.0, 2.0, 1.0], [1.0, 2.0, 1.0], [1.0, 2.0, 0.0], [0.0, 2.0, 0.0]], "3": [[0.0, 3.0, 1.0000000000000002], [1.0, 3.0, 1.0000000000000002], [1.0, 2.0, 1.0], [0.0, 2.0, 1.0]], "4": [[1.0, 3.0, 1.0000000000000002], [1.0, 3.0, 2.220446049250313e-16], [1.0, 2.0, 0.0], [1.0, 2.0, 1.0]], "5": [[0.0, 3.0, 1.0000000000000004], [0.0, 3.0, 4.440892098500626e-16], [1.0, 3.0, 2.220446049250313e-16], [1.0, 3.0, 1.0000000000000002]], "6": [[-6.123233995736766e-17, 2.0, 1.0000000000000007], [-6.123233995736766e-17, 2.0, 6.661338147750939e-16], [0.0, 3.0, 4.440892098500626e-16], [0.0, 3.0, 1.0000000000000004]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": true}, "base_face": "1", "folding_steps": [["2", "1", [0, 2, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["3", "2", [0.0, 2.0, 1.0], [1.0, 0.0, 0.0], -1.5707963267948966], ["4", "3", [1.0, 3.0, 1.0000000000000002], [0.0, -1.0, -2.220446049250313e-16], -1.5707963267948966], ["5", "4", [1.0, 3.0, 1.0000000000000002], [0.0, 0.0, -1.0], -1.5707963267948966], ["6", "5", [0.0, 3.0, 1.0000000000000004], [0.0, 0.0, -1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 3 downwards", "Fold face 4 downwards towards face 1", "Fold face 5 inwards towards face 1", "Fold face 6 inwards towards face 1"], "images_per_step": ["output_dir/folding_nets/net7_base1_step1.png", "output_dir/folding_nets/net7_base1_step2.png", "output_dir/folding_nets/net7_base1_step3.png", "output_dir/folding_nets/net7_base1_step4.png", "output_dir/folding_nets/net7_base1_step5.png", "output_dir/folding_nets/net7_base1_step6.png"], "id": "net7_base1"}	q+steps+all_intermediate_vis	[ "yes", "no" ]
37_q+steps+all_for_valid_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 2 as the base: Step 1: Fold face 1 upwards <image_1> Step 2: Fold face 4 upwards towards face 1 <image_2> Step 3: Fold face 3 inwards towards face 2 <image_3> Step 4: Fold face 5 downwards towards face 1 <image_4> Step 5: Fold face 6 downwards towards face 1 <image_5> 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": {"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]], "2": [[1, 0, 0], [2, 0, 0], [2, 1, 0], [1, 1, 0]], "3": [[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]], "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]], "5": [[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": ["2"], "2": ["1", "4"], "3": ["4"], "4": ["2", "3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": true}, "base_face": "2", "folding_steps": [["1", "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", [2.0, -6.123233995736766e-17, 1.0], [0.0, 6.123233995736766e-17, -1.0], -1.5707963267948966], ["5", "4", [1.0, -6.123233995736766e-17, 1.0], [1.0, 0.0, 0.0], -1.5707963267948966], ["6", "5", [1.0, 0.9999999999999999, 1.0000000000000002], [1.0, 0.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 4 upwards towards face 1", "Fold face 3 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/net4_base2_step1.png", "output_dir/folding_nets/net4_base2_step2.png", "output_dir/folding_nets/net4_base2_step3.png", "output_dir/folding_nets/net4_base2_step4.png", "output_dir/folding_nets/net4_base2_step5.png", "output_dir/folding_nets/net4_base2_step6.png"], "id": "net4_base2"}	q+steps+all_for_valid_vis	[ "no", "yes" ]
16_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 Variant 1", "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, 0.0], [1.0, 1.0, 1.0], [0.0, 1.0, 1.0], [0.0, 1.0, 0.0]]}, "face_connections": {"1": ["4"], "2": ["3"], "3": ["2", "4", "6"], "4": ["1", "3", "5"], "5": ["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", "4", [1.0, 1.0, 1.0], [0.0, 0.0, -1.0], -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 inwards towards face 3"], "images_per_step": ["output_dir/folding_nets/net1_base3_step1.png", "output_dir/folding_nets/net1_base3_step2.png", "output_dir/folding_nets/net1_base3_step3.png", "output_dir/folding_nets/net1_base3_step4.png", "output_dir/folding_nets/net1_base3_step5.png", "output_dir/folding_nets/net1_base3_step6.png"], "id": "net1_base3"}	q_only	[ "no", "yes" ]
140_q+steps+all_for_valid_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 1 as the base: Step 1: Fold face 4 upwards <image_1> Step 2: Fold face 3 inwards towards face 1 <image_2> Step 3: Fold face 2 inwards towards face 1 <image_3> Step 4: Fold face 5 downwards towards face 2 <image_4> Step 5: Fold face 6 downwards towards face 1 <image_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": {"1": [[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0]], "2": [[0.0, 1.0, 0.0], [0.0, 1.0, 1.0], [-2.83276944882399e-16, 0.0, 1.0], [-2.83276944882399e-16, 0.0, 0.0]], "3": [[1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [0.0, 1.0, 1.0], [0.0, 1.0, 0.0]], "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": [[0.9999999999999998, -6.123233995736766e-17, 0.0], [-2.220446049250313e-16, -6.123233995736767e-17, 2.220446049250313e-16], [0.0, 0.0, 1.0000000000000002], [1.0, 0.0, 1.0]]}, "face_connections": {"1": ["4"], "2": ["3"], "3": ["2", "4"], "4": ["1", "3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": true}, "base_face": "1", "folding_steps": [["4", "1", [1, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["3", "4", [1.0, 1.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["2", "3", [0.0, 1.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["5", "4", [1.0, 0.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["6", "5", [1.0, 0.0, 1.0], [-1.0, 0.0, 2.220446049250313e-16], -1.5707963267948966]], "folding_step_descs": ["Fold face 4 upwards", "Fold face 3 inwards towards face 1", "Fold face 2 inwards towards face 1", "Fold face 5 downwards towards face 2", "Fold face 6 downwards towards face 1"], "images_per_step": ["output_dir/folding_nets/net11_base1_step1.png", "output_dir/folding_nets/net11_base1_step2.png", "output_dir/folding_nets/net11_base1_step3.png", "output_dir/folding_nets/net11_base1_step4.png", "output_dir/folding_nets/net11_base1_step5.png", "output_dir/folding_nets/net11_base1_step6.png"], "id": "net11_base1"}	q+steps+all_for_valid_vis	[ "no", "yes" ]
85_q+steps+partial_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 5 as the base: Step 1: Fold face 6 upwards <image_1> 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+partial_vis	[ "no", "yes" ]
110_q+steps+all_intermediate_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 6 as the base: Step 1: Fold face 5 upwards <image_1> Step 2: Fold face 4 inwards towards face 6 <image_2> Step 3: Fold face 3 downwards towards face 5 <image_3> Step 4: Fold face 2 downwards towards face 5 <image_4> 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": [[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]], "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": ["4"], "2": ["3"], "3": ["2", "4"], "4": ["1", "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", "4", [2.0, -1.0, 6.123233995736766e-17], [0.0, 1.1102230246251568e-16, 1.0], 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/net11_base6_step1.png", "output_dir/folding_nets/net11_base6_step2.png", "output_dir/folding_nets/net11_base6_step3.png", "output_dir/folding_nets/net11_base6_step4.png", "output_dir/folding_nets/net11_base6_step5.png", "output_dir/folding_nets/net11_base6_step6.png"], "id": "net11_base6"}	q+steps+all_intermediate_vis	[ "yes", "no" ]
28_q+steps+partial_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 4 as the base: Step 1: Fold face 3 upwards <image_1> Step 2: Fold face 2 downwards Step 3: Fold face 5 upwards towards face 2 Step 4: Fold face 6 inwards 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": "t-shaped Net Variant 2", "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": [[2.0, 0.0, 1.0], [0.9999999999999999, 0.0, 1.0], [0.9999999999999999, 1.0, 1.0], [2.0, 1.0, 1.0]], "4": [[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]], "6": [[2.0, -6.123233995736766e-17, 1.0], [2.0, -6.123233995736766e-17, 1.1102230246251565e-16], [1.0, 0.0, 0.0], [0.9999999999999999, 0.0, 1.0]], "1": [[2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [1.0, 1.0, 1.0], [1.0, 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": "4", "folding_steps": [["3", "4", [1, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "3", [0.9999999999999999, 0.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["5", "4", [2, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["6", "3", [0.9999999999999999, 0.0, 1.0], [1.1102230246251565e-16, 0.0, -1.0], -1.5707963267948966], ["1", "5", [2.0, 1.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 3 upwards", "Fold face 2 downwards", "Fold face 5 upwards towards face 2", "Fold face 6 inwards towards face 2", "Fold face 1 inwards towards face 3"], "images_per_step": ["output_dir/folding_nets/net2_base4_step1.png", "output_dir/folding_nets/net2_base4_step2.png", "output_dir/folding_nets/net2_base4_step3.png", "output_dir/folding_nets/net2_base4_step4.png", "output_dir/folding_nets/net2_base4_step5.png", "output_dir/folding_nets/net2_base4_step6.png"], "id": "net2_base4"}	q+steps+partial_vis	[ "yes", "no" ]
7_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 3 inwards towards face 6 Step 4: Fold face 4 inwards towards face 1 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?	A	{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=0)", "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, -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]], "5": [[-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]], "6": [[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0]]}, "face_connections": {"1": ["2", "6"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4"], "6": ["1"]}, "valid": false}, "base_face": "6", "folding_steps": [["1", "6", [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], ["4", "3", [0.0, -2.83276944882399e-16, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["5", "4", [-1.2246467991473535e-16, 0.9999999999999997, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 2 inwards towards face 6", "Fold face 3 inwards towards face 6", "Fold face 4 inwards towards face 1", "Fold face 5 inwards towards face 1"], "images_per_step": ["output_dir/folding_nets/net13_base6_step1.png", "output_dir/folding_nets/net13_base6_step2.png", "output_dir/folding_nets/net13_base6_step3.png", "output_dir/folding_nets/net13_base6_step4.png"], "id": "net13_base6"}	q+steps	[ "no", "yes" ]
38_q+steps+all_for_valid_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 5 as the base: Step 1: Fold face 6 upwards <image_1> Step 2: Fold face 3 upwards towards face 6 <image_2> Step 3: Fold face 4 upwards towards face 3 <image_3> Step 4: Fold face 2 downwards towards face 3 <image_4> Step 5: Fold face 1 downwards towards face 4 <image_5> 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": [[0.9999999999999999, -0.9999999999999999, 0.0], [1.0, -0.9999999999999999, 1.0], [1.0, -2.0, 1.0], [0.9999999999999999, -2.0, 0.0]], "2": [[1.0, -0.9999999999999999, 1.0], [2.0, -0.9999999999999999, 1.0], [2.0, -2.0, 1.0], [1.0, -2.0, 1.0]], "3": [[2.0, -2.0, 0.0], [2.0, -2.0, 1.0], [2.0, -1.0, 1.0], [2.0, -1.0, 0.0]], "4": [[1.0, -1.0, 0.0], [2.0, -1.0, 0.0], [2.0, -0.9999999999999999, 1.0], [1.0, -0.9999999999999999, 1.0]], "5": [[1, -2, 0], [2, -2, 0], [2, -1, 0], [1, -1, 0]], "6": [[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": {"1": ["2"], "2": ["1", "4"], "3": ["5"], "4": ["2", "5"], "5": ["4", "3", "6"], "6": ["5"]}, "valid": true}, "base_face": "5", "folding_steps": [["6", "5", [1, -2, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["3", "5", [2, -2, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "5", [2, -1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["2", "4", [2.0, -0.9999999999999999, 1.0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["1", "2", [1.0, -0.9999999999999999, 1.0], [0.0, -1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 3 upwards towards face 6", "Fold face 4 upwards towards face 3", "Fold face 2 downwards towards face 3", "Fold face 1 downwards towards face 4"], "images_per_step": ["output_dir/folding_nets/net5_base5_step1.png", "output_dir/folding_nets/net5_base5_step2.png", "output_dir/folding_nets/net5_base5_step3.png", "output_dir/folding_nets/net5_base5_step4.png", "output_dir/folding_nets/net5_base5_step5.png", "output_dir/folding_nets/net5_base5_step6.png"], "id": "net5_base5"}	q+steps+all_for_valid_vis	[ "yes", "no" ]
42_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 4 upwards Step 2: Fold face 3 downwards Step 3: Fold face 2 downwards towards face 5 Step 4: Fold face 1 upwards towards face 4 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=0)", "faces": {"1": [[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]], "2": [[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]], "4": [[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]], "6": [[3.999999999999999, 0.9999999999999999, 0.999999999999999], [4.999999999999999, 0.9999999999999999, 0.9999999999999999], [5.0, 1.0, -1.9721522630525295e-31], [4.0, 1.0, -9.494107596574928e-16]]}, "face_connections": {"1": ["2", "6"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4"], "6": ["1"]}, "valid": false}, "base_face": "5", "folding_steps": [["4", "5", [4, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "4", [4.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "3", [5.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["1", "2", [5.0, 1.0, 0.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["6", "1", [4.0, 1.0, -9.494107596574928e-16], [1.0, 0.0, 9.494107596574928e-16], -1.5707963267948966]], "folding_step_descs": ["Fold face 4 upwards", "Fold face 3 downwards", "Fold face 2 downwards towards face 5", "Fold face 1 upwards towards face 4", "Fold face 6 upwards towards face 2"], "images_per_step": ["output_dir/folding_nets/net13_base5_step1.png", "output_dir/folding_nets/net13_base5_step2.png", "output_dir/folding_nets/net13_base5_step3.png"], "id": "net13_base5"}	q+steps	[ "yes", "no" ]
7_q+steps+partial_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 6 as the base: Step 1: Fold face 1 upwards <image_1> Step 2: Fold face 2 inwards towards face 6 <image_2> Step 3: Fold face 3 inwards towards face 6 Step 4: Fold face 4 inwards towards face 1 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": "Net B: Row 5 + Face 6 (shift=0)", "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, -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]], "5": [[-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]], "6": [[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0]]}, "face_connections": {"1": ["2", "6"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4"], "6": ["1"]}, "valid": false}, "base_face": "6", "folding_steps": [["1", "6", [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], ["4", "3", [0.0, -2.83276944882399e-16, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["5", "4", [-1.2246467991473535e-16, 0.9999999999999997, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 2 inwards towards face 6", "Fold face 3 inwards towards face 6", "Fold face 4 inwards towards face 1", "Fold face 5 inwards towards face 1"], "images_per_step": ["output_dir/folding_nets/net13_base6_step1.png", "output_dir/folding_nets/net13_base6_step2.png", "output_dir/folding_nets/net13_base6_step3.png", "output_dir/folding_nets/net13_base6_step4.png"], "id": "net13_base6"}	q+steps+partial_vis	[ "yes", "no" ]
65_q+steps+partial_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 2 as the base: Step 1: Fold face 1 upwards <image_1> Step 2: Fold face 3 upwards towards face 1 <image_2> Step 3: Fold face 4 downwards towards face 1 Step 4: Fold face 5 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?	B	{"initial_net": {"name": "invalid_E", "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]], "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]], "2": [[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]], "4": [[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": {"1": ["2"], "6": ["5"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4", "6"]}, "valid": false}, "base_face": "2", "folding_steps": [["1", "2", [1, 1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["3", "2", [1, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "3", [1.0, 0.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["5", "4", [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 1 upwards", "Fold face 3 upwards towards face 1", "Fold face 4 downwards towards face 1", "Fold face 5 downwards towards face 1", "Fold face 6 downwards towards face 1"], "images_per_step": ["output_dir/folding_nets/net22_base2_step1.png", "output_dir/folding_nets/net22_base2_step2.png", "output_dir/folding_nets/net22_base2_step3.png", "output_dir/folding_nets/net22_base2_step4.png"], "id": "net22_base2"}	q+steps+partial_vis	[ "yes", "no" ]
96_q+steps+all_intermediate_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 1 as the base: Step 1: Fold face 2 upwards <image_1> Step 2: Fold face 3 downwards <image_2> Step 4: Fold face 5 upwards towards face 1 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": "Net B: Row 5 + Face 6 (shift=4)", "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": [[-1.6081226496766364e-16, 0.9999999999999999, 1.0000000000000002], [0.9999999999999999, 0.9999999999999999, 1.0], [0.9999999999999997, 1.0, 9.957992501029599e-17], [-2.83276944882399e-16, 1.0, 2.220446049250313e-16]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": false}, "base_face": "1", "folding_steps": [["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], ["6", "5", [-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [1.0, 0.0, -1.2246467991473535e-16], -1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 3 downwards", "Fold face 4 downwards towards face 1", "Fold face 5 upwards towards face 1", "Fold face 6 upwards towards face 1"], "images_per_step": ["output_dir/folding_nets/net17_base1_step1.png", "output_dir/folding_nets/net17_base1_step2.png", "output_dir/folding_nets/net17_base1_step3.png"], "id": "net17_base1"}	q+steps+all_intermediate_vis	[ "yes", "no" ]
81_q+steps+all_intermediate_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 3 as the base: Step 1: Fold face 2 upwards <image_1> Step 2: Fold face 4 upwards <image_2> Step 3: Fold face 5 upwards towards face 2 <image_3> 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?	A	{"initial_net": {"name": "invalid_F", "faces": {"1": [[3.0, 1.0, 1.0000000000000002], [2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [3.0, 2.0, 1.0000000000000002]], "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]], "3": [[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": [[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, 1.0, 1.0], [2.0, 1.0, 1.0], [2.0, 1.0, 6.123233995736766e-17], [3.0, 1.0, 0.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4", "5"], "4": ["3", "6"], "5": ["3", "6"], "6": ["4", "5"]}, "valid": false}, "base_face": "3", "folding_steps": [["2", "3", [2, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["4", "3", [3, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["5", "3", [2, 1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["6", "4", [3.0, 1.0, 0.0], [0.0, 0.0, 1.0], 1.5707963267948966], ["1", "2", [2.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 4 upwards", "Fold face 5 upwards towards face 2", "Fold face 6 inwards towards face 2", "Fold face 1 downwards towards face 4"], "images_per_step": ["output_dir/folding_nets/net21_base3_step1.png", "output_dir/folding_nets/net21_base3_step2.png", "output_dir/folding_nets/net21_base3_step3.png", "output_dir/folding_nets/net21_base3_step4.png"], "id": "net21_base3"}	q+steps+all_intermediate_vis	[ "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?	B	{"initial_net": {"name": "Big T Net", "faces": {"1": [[3.0, 0.0, 1.0000000000000002], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [3.0, 1.0, 1.0000000000000002]], "2": [[2.0, 0.0, 1.0], [2.0, 0.0, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, 1.0]], "3": [[2, 0, 0], [3, 0, 0], [3, 1, 0], [2, 1, 0]], "4": [[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]], "5": [[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]], "6": [[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": {"1": ["2"], "2": ["1", "3", "4"], "3": ["2"], "4": ["2", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": true}, "base_face": "3", "folding_steps": [["2", "3", [2, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["4", "2", [2.0, 0.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["5", "4", [3.0, -6.123233995736766e-17, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["6", "5", [3.0, 0.9999999999999999, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["1", "2", [2.0, 0.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 4 inwards towards face 3", "Fold face 5 inwards towards face 3", "Fold face 6 inwards towards face 2", "Fold face 1 downwards towards face 4"], "images_per_step": ["output_dir/folding_nets/net3_base3_step1.png", "output_dir/folding_nets/net3_base3_step2.png", "output_dir/folding_nets/net3_base3_step3.png", "output_dir/folding_nets/net3_base3_step4.png", "output_dir/folding_nets/net3_base3_step5.png", "output_dir/folding_nets/net3_base3_step6.png"], "id": "net3_base3"}	q_only	[ "no", "yes" ]
48_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": {"1": [[3.0, 0.9999999999999998, 1.0], [2.0, 1.0, 1.0], [2.0, 0.9999999999999999, 0.0], [3.0, 0.9999999999999997, 2.220446049250313e-16]], "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]], "3": [[2, 1, 0], [3, 1, 0], [3, 2, 0], [2, 2, 0]], "4": [[3.0, 2.0, 1.0], [2.0, 2.0, 1.0], [2.0, 1.0, 1.0], [3.0, 0.9999999999999998, 1.0]], "5": [[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]], "6": [[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": {"1": ["2", "4"], "2": ["1", "3", "5"], "3": ["2", "6"], "4": ["1", "5"], "5": ["2", "4", "6"], "6": ["3", "5"]}, "valid": false}, "base_face": "3", "folding_steps": [["6", "3", [2, 1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["2", "3", [2, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["5", "2", [2.0, 1.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["4", "5", [2.0, 2.0, 1.0], [0.0, -1.0, 0.0], -1.5707963267948966], ["1", "4", [2.0, 1.0, 1.0], [1.0, -2.220446049250313e-16, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 2 upwards towards face 6", "Fold face 5 inwards towards face 3", "Fold face 4 downwards towards face 2", "Fold face 1 downwards towards face 3"], "images_per_step": ["output_dir/folding_nets/net18_base3_step1.png", "output_dir/folding_nets/net18_base3_step2.png"], "id": "net18_base3"}	q_only	[ "yes", "no" ]
15_q+steps+all_intermediate_vis	Check out a net with 6 faces below: <image_0>Here are the steps to fold the net with face 2 as the base: Step 1: Fold face 1 upwards <image_1> Step 2: Fold face 3 upwards <image_2> Step 4: Fold face 5 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": "Net B: Row 5 + Face 6 (shift=3)", "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": [[2.0, 0.9999999999999999, 0.0], [1.0, 0.9999999999999999, 0.0], [1.0, 1.0, 1.0], [2.0, 1.0, 1.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5", "6"], "5": ["4"], "6": ["4"]}, "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", "4", [2.0, 1.0, 1.0], [-1.0, 0.0, 0.0], -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 downwards towards face 1"], "images_per_step": ["output_dir/folding_nets/net16_base2_step1.png", "output_dir/folding_nets/net16_base2_step2.png", "output_dir/folding_nets/net16_base2_step3.png"], "id": "net16_base2"}	q+steps+all_intermediate_vis	[ "no", "yes" ]