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2
141_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 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> Step 5: Fold fa...
B
{"initial_net": {"name": "t-shaped Net Variant 1", "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, -0.9999999...
q+steps+all_for_valid_vis
[ "no", "yes" ]
39_q+steps
Check out a net with 6 faces below: <image_0>Below are the steps to fold the net with face 3 as the base: Step 1: Fold face 2 upwards Step 2: Fold face 4 upwards towards face 2 Step 3: Fold face 5 inwards towards face 3 Step 4: Fold face 6 inwards towards face 2 Step 5: Fold face 1 downwards towards face 4 Based on th...
A
{"initial_net": {"name": "3-3 Net", "faces": {"1": [[0.0, 1.0, 1.0], [1.0, 1.0, 1.0], [1.0, 0.0, 1.0000000000000002], [0.0, 0.0, 1.0000000000000002]], "2": [[0.0, 1.0, 0.0], [1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [0.0, 1.0, 1.0]], "3": [[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0]], "4": [[1.0, 0.0, 0.0], [1.0, 0.0, 1.0], [1....
q+steps
[ "yes", "no" ]
19_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 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 2 <image_3> Step 4: Fold face 6 inwards towards face 2 <image_4> Step 5: Fold face 1 inwards to...
B
{"initial_net": {"name": "t-shaped Net", "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]], "1": [[0.9999999999999999, 1.0, 1.0], [1.0, 1.0, 0.0], [2.0, 1.0, 1.1102230246251565e-16], [2.0, 1.0, 1.0]], "2": [[2.0, 0.0, 1.0], [0.9999999999999999, 0.0, 1.0], ...
q+steps+all_for_valid_vis
[ "no", "yes" ]
75_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 3: Fold face 5 upwards towards face 2 <image_3> Step 4: Fold face 6 inwards towards face 2 <image_4> Based on the above steps, can ...
B
{"initial_net": {"name": "1-3-2 Net", "faces": {"1": [[0.9999999999999999, 0.9999999999999998, 0.0], [1.0, 1.0, 1.0], [1.0, 0.0, 1.0000000000000002], [0.9999999999999999, -2.220446049250313e-16, 2.220446049250313e-16]], "2": [[1.0, 1.0, 1.0], [2.0, 1.0, 1.0], [2.0, 0.0, 1.0000000000000002], [1.0, 0.0, 1.000000000000000...
q+steps+all_intermediate_vis
[ "no", "yes" ]
99_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 inwards towards face 3 Step 3: Fold face 5 upwards towards face 2 Step 4: Fold face 6 upwards towards face 3 Step 5: Fold face 1 downwards towards face 4 Ba...
A
{"initial_net": {"name": "Net H: Two rows with bottom row shifted right", "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": ...
q+steps+partial_vis
[ "no", "yes" ]
111_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 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> Step 5: Fold fa...
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], [...
q+steps+all_for_valid_vis
[ "no", "yes" ]
27_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 1 upwards <image_1> Step 3: Fold face 3 inwards towards face 4 Step 4: Fold face 5 upwards towards face 1 Step 5: Fold face 6 inwards Based on the above steps, can the net be folded to form a cube...
B
{"initial_net": {"name": "2 Rows of 3", "faces": {"1": [[0.0, 1.0, 0.0], [1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [0.0, 1.0, 1.0]], "2": [[1.0, 1.0, 0.0], [1.0, 0.0, 0.0], [1.0, 0.0, 1.0], [1.0, 1.0, 1.0]], "3": [[1.0, 0.0, 0.0], [0.0, -2.83276944882399e-16, 0.0], [0.0, -2.83276944882399e-16, 1.0], [1.0, 0.0, 1.0]], "4": [[0,...
q+steps+all_intermediate_vis
[ "yes", "no" ]
70_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 upwards <image_2> Step 3: Fold face 5 inwards towards face 2 <image_3> Step 4: Fold face 6 downwards towards face 2 <image_4> Step 5: Fold face 1 upwards to...
B
{"initial_net": {"name": "1-3-2 Net", "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": [[1.0, 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....
q+steps+all_for_valid_vis
[ "no", "yes" ]
88_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 2 upwards towards face 6 <image_2> Step 3: Fold face 4 upwards towards face 6 <image_3> Step 4: Fold face 5 downwards towards face 2 <image_4> Step 5: Fold fa...
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...
q+steps+all_for_valid_vis
[ "no", "yes" ]
125_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 5: Fold face 1 inwards towards face 3 Based on the above steps, c...
B
{"initial_net": {"name": "Invalid D", "faces": {"1": [[2.0, 0.9999999999999999, -1.0], [2.0, 0.9999999999999999, -1.1102230246251565e-16], [1.0, 1.0, 0.0], [0.9999999999999999, 1.0, -1.0]], "2": [[0.9999999999999999, 1.0, -1.0], [1.0, 1.0, 0.0], [1.0, 2.0, 0.0], [0.9999999999999999, 2.0, -1.0]], "3": [[1, 1, 0], [1, 2,...
q+steps+all_intermediate_vis
[ "yes", "no" ]
104_q+steps
Check out a net with 6 faces below: <image_0>Below are the steps to fold the net with face 4 as the base: Step 1: Fold face 3 upwards Step 2: Fold face 2 downwards Step 3: Fold face 5 upwards towards face 1 Step 4: Fold face 1 downwards towards face 4 Step 5: Fold face 6 inwards towards face 2 Based on the above steps...
B
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=0)", "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...
q+steps
[ "yes", "no" ]
119_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 2 upwards <image_1> Step 2: Fold face 4 inwards towards face 1 <image_2> Step 3: Fold face 3 downwards towards face 4 Step 4: Fold face 5 inwards towards face 1 Step 5: Fold face 6 inwards towards...
A
{"initial_net": {"name": "Big T Net", "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": [[1.0, 0.0, 1.0], [0.0, 0.0, 1.0000000000000002], [0.0, 1.0, 1.0000000000000002], [1.0, 1.0, 1.0]], "4": [[0.0, -6.123233995736766e-17, 0.0],...
q+steps+partial_vis
[ "yes", "no" ]
141_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 ab...
A
{"initial_net": {"name": "t-shaped Net Variant 1", "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, -0.9999999...
q+steps+all_intermediate_vis
[ "yes", "no" ]
64_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 2 Step 4: Fold face 6 downwards towards face 1 Step 5: Fold face 1 inwards towards face 6 Based on the above steps...
A
{"initial_net": {"name": "invalid_E", "faces": {"1": [[0.9999999999999999, 1.0, 1.0], [1.0, 1.0, 0.0], [2.0, 1.0, 1.1102230246251565e-16], [2.0, 1.0, 1.0]], "6": [[2.0, 1.0, 1.0], [1.0, 1.0, 1.0], [1.0, 1.0, 0.0], [2.0, 1.0, 0.0]], "2": [[0.9999999999999999, 0.0, 1.0], [1.0, 0.0, 0.0], [1.0, 1.0, 0.0], [0.9999999999999...
q+steps
[ "no", "yes" ]
130_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 upwards towards face 1 Step 5: Fold face 6 upwards towards face 1 Based on the above steps...
A
{"initial_net": {"name": "Linear 6-Face Row", "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": [[1.0, 0.0, 1.0], [0.0, 0.0, 1.0000000000000002], [0.0, 1.0, 1.0000000000000002], [1.0, 1.0, 1.0]], "4": [[0.0, 0.0, 1.00000000000000...
q+steps
[ "no", "yes" ]
101_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 3 upwards <image_1> Step 2: Fold face 4 downwards <image_2> Step 3: Fold face 5 downwards towards face 2 <image_3> Step 4: Fold face 6 inwards towards face 2 <image_4> Based on the above steps, ca...
B
{"initial_net": {"name": "1-3-2 Net", "faces": {"1": [[0.9999999999999999, 3.0, 1.0], [1.0, 2.0, 1.0], [1.0, 2.0, 0.0], [0.9999999999999999, 3.0, 0.0]], "2": [[1, 2, 0], [2, 2, 0], [2, 3, 0], [1, 3, 0]], "3": [[1.0, 2.0, 1.0], [2.0, 2.0, 1.0], [2.0, 2.0, 0.0], [1.0, 2.0, 0.0]], "4": [[1.0, 3.0, 1.0000000000000002], [2....
q+steps+all_intermediate_vis
[ "no", "yes" ]
36_q+steps
Check out a net with 6 faces below: <image_0>Below are the steps to fold the net with face 6 as the base: Step 1: Fold face 5 upwards Step 2: Fold face 3 inwards towards face 6 Step 3: Fold face 2 downwards towards face 5 Step 4: Fold face 4 downwards towards face 3 Step 5: Fold face 1 downwards towards face 4 Based o...
B
{"initial_net": {"name": "Net H: Two rows with bottom row shifted right", "faces": {"1": [[3.0, -2.83276944882399e-16, 0.0], [3.0, 0.0, 1.0], [4.0, 0.0, 1.0], [4.0, -2.83276944882399e-16, 0.0]], "2": [[3.0, 0.0, 1.0], [3.0, 1.0, 1.0], [4.0, 1.0, 1.0], [4.0, 0.0, 1.0]], "3": [[3.0, 1.0, 1.0], [3.0, 1.0, 0.0], [4.0, 1.0,...
q+steps
[ "yes", "no" ]
109_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 downwards towards face 1 Step 5: Fold face 1 downwards towards face 3 Based on ...
A
{"initial_net": {"name": "Invalid D", "faces": {"1": [[2.0, 3.0, 1.0000000000000002], [2.0, 2.0, 1.0000000000000002], [1.0, 2.0, 1.0], [0.9999999999999999, 3.0, 1.0]], "2": [[0.9999999999999999, 3.0, 1.0], [1.0, 2.0, 1.0], [1.0, 2.0, 0.0], [0.9999999999999999, 3.0, 0.0]], "3": [[1.0, 2.0, 1.0], [1.0, 2.0, 0.0], [2.0, 2...
q+steps
[ "no", "yes" ]
66_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 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> Step 5: Fold face 1 upward...
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, 2.220446...
q+steps+all_for_valid_vis
[ "no", "yes" ]
105_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 6 upwards <image_1> Step 2: Fold face 2 upwards towards face 6 <image_2> Step 3: Fold face 3 downwards towards face 6 <image_3> Step 5: Fold face 5 upwards towards face 1 Based on the above steps,...
B
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=0)", "faces": {"1": [[0, 1, 0], [1, 1, 0], [1, 2, 0], [0, 2, 0]], "2": [[1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [1.0, 2.0, 1.0], [1.0, 2.0, 0.0]], "3": [[1.0, 1.0, 1.0], [0.0, 1.0, 1.0000000000000002], [0.0, 2.0, 1.0000000000000002], [1.0, 2.0, 1.0]], "4": [[0.0, 1.0, 1....
q+steps+all_intermediate_vis
[ "yes", "no" ]
47_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 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> Step 5: Fold fa...
B
{"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, -0.9999999...
q+steps+all_for_valid_vis
[ "no", "yes" ]
20_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 4 upwards towards face 1 Step 3: Fold face 3 upwards towards face 4 Step 4: Fold face 5 downwards towards face 1 Step 5: Fold face 6 downwards towards face 1 Based on ...
B
{"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],...
q+steps
[ "no", "yes" ]
24_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 4 upwards <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 downward...
A
{"initial_net": {"name": "Big T Net", "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, -0.999999999...
q+steps+all_for_valid_vis
[ "yes", "no" ]
135_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 3: Fold face 5 upwards towards face 2 <image_3> Step 5: Fold face 1 downwards towards face 3 Based on the above steps, can the net ...
B
{"initial_net": {"name": "invalid_G", "faces": {"2": [[3.0, 0.0, 1.0000000000000002], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [3.0, 1.0, 1.0000000000000002]], "3": [[2.0, 0.0, 1.0], [2.0, 0.0, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, 1.0]], "4": [[2, 0, 0], [3, 0, 0], [3, 1, 0], [2, 1, 0]], "5": [[3.0, 0.0, 0.0], [3.0, 0.0, 1.0], [...
q+steps+all_intermediate_vis
[ "yes", "no" ]
115_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, ...
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, 2.220446...
q+steps+all_intermediate_vis
[ "no", "yes" ]
2_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 downwards <image_2> Step 3: Fold face 3 downwards towards face 5 Step 4: Fold face 2 downwards towards face 3 Step 5: Fold face 1 downwards towards face 4 B...
B
{"initial_net": {"name": "Big T - Variant 1", "faces": {"1": [[0.9999999999999999, -2.0, 0.9999999999999998], [1.0, -3.0, 1.0000000000000002], [1.0, -3.0000000000000004, 2.220446049250313e-16], [0.9999999999999999, -2.0000000000000004, -2.220446049250313e-16]], "2": [[1.0, -3.0, 1.0000000000000002], [2.0, -3.0, 1.00000...
q+steps+partial_vis
[ "no", "yes" ]
67_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 4 upwards towards face 1 Step 3: Fold face 5 downwards towards face 1 Step 4: Fold face 6 downwards towards face 1 Step 5: Fold face 3 inwards towards face 2 Based on ...
B
{"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, 0.999999...
q+steps
[ "no", "yes" ]
83_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 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> Step 5: Fold ...
B
{"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, 1.00000...
q+steps+all_for_valid_vis
[ "no", "yes" ]
26_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 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 Ba...
B
{"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"...
q+steps+partial_vis
[ "no", "yes" ]
100_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 upwards <image_2> Step 3: Fold face 5 inwards towards face 2 <image_3> Step 4: Fold face 6 downwards towards face 2 <image_4> Step 5: Fold face 1 inwards to...
B
{"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....
q+steps+all_for_valid_vis
[ "no", "yes" ]
52_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 inwards towards face 2 <image_2> Step 4: Fold face 5 upwards towards face 1 Step 5: Fold face 6 inwards towards face 1 Based on the above steps, can the net...
B
{"initial_net": {"name": "2 Rows of 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, 0.9999999999999999, 1.0], [...
q+steps+all_intermediate_vis
[ "yes", "no" ]
57_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 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...
A
{"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],...
q+steps+partial_vis
[ "yes", "no" ]
73_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 3 inwards towards face 4 Step 3: Fold face 5 upwards towards face 2 Step 4: Fold face 6 downwards towards face 2 Step 5: Fold face 1 inwards towards face 4 Ba...
A
{"initial_net": {"name": "Net H: Two rows with bottom row shifted right", "faces": {"1": [[0.9999999999999999, 0.0, 0.0], [1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [0.9999999999999999, 0.0, 1.0]], "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, 0.0, 0.0], [2.0, 0.0, 1.0],...
q+steps+partial_vis
[ "no", "yes" ]
17_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 2 upwards <image_1> Step 2: Fold face 3 downwards Step 3: Fold face 4 downwards towards face 1 Step 4: Fold face 5 upwards towards face 1 Step 5: Fold face 6 inwards towards face 1 Based on the ab...
B
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=1)", "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....
q+steps+partial_vis
[ "yes", "no" ]
2_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 downwards <image_2> Step 3: Fold face 3 downwards towards face 5 <image_3> Step 4: Fold face 2 downwards towards face 3 <image_4> Based on the above steps, ...
B
{"initial_net": {"name": "Big T - Variant 1", "faces": {"1": [[0.9999999999999999, -2.0, 0.9999999999999998], [1.0, -3.0, 1.0000000000000002], [1.0, -3.0000000000000004, 2.220446049250313e-16], [0.9999999999999999, -2.0000000000000004, -2.220446049250313e-16]], "2": [[1.0, -3.0, 1.0000000000000002], [2.0, -3.0, 1.00000...
q+steps+all_intermediate_vis
[ "no", "yes" ]
139_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 3: Fold face 2 inwards towards face 5 Step 4: Fold face 4 inwards towards face 1 Step 5: Fold face 1 inwards towards face 4 Based on the above steps, can the net be folded...
A
{"initial_net": {"name": "invalid_F", "faces": {"1": [[3.0, -2.83276944882399e-16, 0.0], [2.0, 0.0, 0.0], [2.0, 0.0, 1.0], [3.0, -2.83276944882399e-16, 1.0]], "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": [[2.0,...
q+steps+all_intermediate_vis
[ "no", "yes" ]
104_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 1 Step 4: Fold face 1 downwards towards face 4 Step 5: Fold face 6 inwards towards face 2 Based on the ab...
A
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=0)", "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...
q+steps+partial_vis
[ "no", "yes" ]
10_q+steps
Check out a net with 6 faces below: <image_0>Below are the steps to fold the net with face 2 as the base: Step 1: Fold face 3 upwards Step 2: Fold face 4 downwards Step 3: Fold face 5 downwards towards face 2 Step 4: Fold face 6 inwards towards face 2 Step 5: Fold face 1 downwards towards face 2 Based on the above ste...
B
{"initial_net": {"name": "1-3-2 Net", "faces": {"1": [[0.9999999999999999, 3.0, 2.220446049250313e-16], [1.0, 3.0, 1.0000000000000002], [1.0, 2.0, 1.0], [0.9999999999999999, 2.0, 0.0]], "2": [[1, 2, 0], [2, 2, 0], [2, 3, 0], [1, 3, 0]], "3": [[1.0, 2.0, 1.0], [2.0, 2.0, 1.0], [2.0, 2.0, 0.0], [1.0, 2.0, 0.0]], "4": [[1...
q+steps
[ "no", "yes" ]
50_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 3 upwards <image_1> Step 2: Fold face 4 downwards <image_2> Step 3: Fold face 5 downwards towards face 2 <image_3> Step 4: Fold face 6 inwards towards face 2 <image_4> Step 5: Fold face 1 inwards ...
A
{"initial_net": {"name": "t-shaped Net", "faces": {"3": [[0.0, 0.0, 0.0], [6.123233995736766e-17, 0.0, 1.0], [6.123233995736766e-17, 1.0, 1.0], [0.0, 1.0, 0.0]], "1": [[1.232595164407831e-32, 1.0, 0.0], [6.123233995736766e-17, 1.0, 1.0], [-0.9999999999999999, 1.0, 1.0], [-0.9999999999999999, 1.0, 1.1102230246251565e-16...
q+steps+all_for_valid_vis
[ "yes", "no" ]
108_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 downwards towards face 2 Step 5: Fold face 1 downwards towards face 4 Based on ...
A
{"initial_net": {"name": "3-3 Net", "faces": {"1": [[2.0, 1.0, 1.0], [2.0, 1.0, 1.1102230246251565e-16], [2.0000000000000004, 0.0, 2.220446049250313e-16], [2.0000000000000004, 0.0, 1.0]], "2": [[0.9999999999999999, 1.0, 1.0], [1.0, 1.0, 0.0], [2.0, 1.0, 1.1102230246251565e-16], [2.0, 1.0, 1.0]], "3": [[0.99999999999999...
q+steps
[ "yes", "no" ]
90_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 6 upwards Step 2: Fold face 3 upwards towards face 6 Step 3: Fold face 4 downwards towards face 6 Step 4: Fold face 5 downwards towards face 1 Step 5: Fold face 1 upwards towards face 4 Based on ...
A
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=1)", "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....
q+steps
[ "no", "yes" ]
92_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 inwards towards face 4 <image_2> Step 3: Fold face 5 upwards towards face 3 <image_3> Step 4: Fold face 6 inwards towards face 2 <image_4> Based on the abov...
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":...
q+steps+all_intermediate_vis
[ "no", "yes" ]
6_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 inwards towards face 1 <image_3> Step 5: Fold face 6 upwards towards face 1 Based on the above steps, c...
B
{"initial_net": {"name": "invalid_E", "faces": {"1": [[0, 1, 0], [1, 1, 0], [1, 2, 0], [0, 2, 0]], "6": [[-1.232595164407831e-32, 2.0000000000000004, 2.220446049250313e-16], [-6.123233995736766e-17, 1.0000000000000004, 3.3306690738754696e-16], [0.9999999999999998, 1.0000000000000004, 2.718345674301793e-16], [0.99999999...
q+steps+all_intermediate_vis
[ "yes", "no" ]
42_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 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 ab...
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,...
q+steps+partial_vis
[ "yes", "no" ]
61_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 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> Step 5: Fold fa...
B
{"initial_net": {"name": "t-shaped Net", "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]], "1": [[0.0, 6.123233995736766e-17, 1.0], [1.0, 6.123233995736766e-17, 1.0], [1.0, -0.9999999999999999, 1.0000000000000002], [0.0, -0.9999999999999999, 1.00000...
q+steps+all_for_valid_vis
[ "no", "yes" ]
66_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 <image_3> Step 4: Fold face 6 downwards towards face 2 <image_4> Step 5: Fold face 1 upward...
A
{"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, 2.220446...
q+steps+partial_vis
[ "yes", "no" ]
97_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 3 upwards <image_1> Step 2: Fold face 6 inwards towards face 2 <image_2> Step 3: Fold face 4 downwards towards face 6 <image_3> Step 4: Fold face 5 downwards towards face 2 <image_4> Based on the ...
A
{"initial_net": {"name": "t-shaped Net Variant 1", "faces": {"3": [[0.0, 0.0, 0.0], [6.123233995736766e-17, 0.0, 1.0], [6.123233995736766e-17, 1.0, 1.0], [0.0, 1.0, 0.0]], "2": [[-1, 0, 0], [0, 0, 0], [0, 1, 0], [-1, 1, 0]], "4": [[6.123233995736766e-17, 0.0, 1.0], [-0.9999999999999999, 0.0, 1.0000000000000002], [-0.99...
q+steps+all_intermediate_vis
[ "yes", "no" ]
124_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 inwards towards face 2 <image_3> Step 4: Fold face 6 downwards towards face 2 <image_4> Based on the above steps, can ...
B
{"initial_net": {"name": "1-3-2 Net", "faces": {"1": [[0.9999999999999999, 2.0, 1.0], [1.0, 0.9999999999999999, 1.0], [1.0, 1.0, 0.0], [0.9999999999999999, 2.0, 1.1102230246251565e-16]], "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": [[...
q+steps+all_intermediate_vis
[ "no", "yes" ]
77_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 downwards <image_2> Step 3: Fold face 3 downwards towards face 5 <image_3> Step 5: Fold face 1 upwards towards face 3 Based on the above steps, can the net ...
B
{"initial_net": {"name": "Invalid D", "faces": {"1": [[3.0, 3.0, -9.494107596574928e-16], [3.0, 2.0, -6.123233995736766e-17], [4.0, 2.0, 0.0], [4.0, 3.0, 0.0]], "2": [[4.0, 3.0, 0.0], [4.0, 2.0, 0.0], [4.0, 2.0, 1.0], [4.0, 3.0, 1.0]], "3": [[4.0, 2.0, 0.0], [4.0, 2.0, 1.0], [3.0, 2.0, 1.0], [3.0, 2.0, 0.0]], "4": [[4....
q+steps+all_intermediate_vis
[ "yes", "no" ]
130_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 2 upwards <image_1> Step 2: Fold face 3 downwards Step 3: Fold face 4 downwards towards face 1 Step 4: Fold face 5 upwards towards face 1 Step 5: Fold face 6 upwards towards face 1 Based on the ab...
B
{"initial_net": {"name": "Linear 6-Face Row", "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": [[1.0, 0.0, 1.0], [0.0, 0.0, 1.0000000000000002], [0.0, 1.0, 1.0000000000000002], [1.0, 1.0, 1.0]], "4": [[0.0, 0.0, 1.00000000000000...
q+steps+partial_vis
[ "yes", "no" ]
39_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 upwards towards face 2 <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...
B
{"initial_net": {"name": "3-3 Net", "faces": {"1": [[0.0, 1.0, 1.0], [1.0, 1.0, 1.0], [1.0, 0.0, 1.0000000000000002], [0.0, 0.0, 1.0000000000000002]], "2": [[0.0, 1.0, 0.0], [1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [0.0, 1.0, 1.0]], "3": [[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0]], "4": [[1.0, 0.0, 0.0], [1.0, 0.0, 1.0], [1....
q+steps+all_for_valid_vis
[ "no", "yes" ]
127_q+steps
Check out a net with 6 faces below: <image_0>Below are the steps to fold the net with face 5 as the base: Step 1: Fold face 6 upwards Step 2: Fold face 4 upwards towards face 6 Step 3: Fold face 3 inwards towards face 5 Step 4: Fold face 2 inwards towards face 5 Step 5: Fold face 1 downwards towards face 2 Based on th...
A
{"initial_net": {"name": "1-3-2 Net", "faces": {"1": [[2.0, 0.0, 1.0000000000000002], [2.0, 1.0, 1.0], [3.0, 1.0, 1.0], [3.0, 0.0, 1.0000000000000002]], "2": [[3.0, 1.0, 1.0], [3.0, 1.0, 0.0], [3.0000000000000004, 0.0, 0.0], [3.0000000000000004, 0.0, 1.0]], "3": [[2.0, 1.0, 1.0], [2.0, 1.0, 0.0], [3.0, 1.0, 0.0], [3.0,...
q+steps
[ "yes", "no" ]
142_q+steps
Check out a net with 6 faces below: <image_0>Below are the steps to fold the net with face 6 as the base: Step 1: Fold face 5 upwards Step 2: Fold face 4 inwards towards face 6 Step 3: Fold face 3 inwards towards face 6 Step 4: Fold face 2 inwards towards face 5 Step 5: Fold face 1 inwards towards face 4 Based on the ...
B
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=4)", "faces": {"1": [[4.0, 1.0000000000000009, 0.0], [5.0, 0.9999999999999999, 0.0], [5.0, 0.9999999999999999, 1.0], [4.0, 1.0000000000000009, 1.0]], "2": [[5.0, 0.9999999999999999, 0.0], [5.0, -6.123233995736766e-17, 0.0], [5.0, -6.123233995736766e-17, 1.0], [5.0,...
q+steps
[ "yes", "no" ]
124_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 upwards <image_2> Step 3: Fold face 5 inwards towards face 2 <image_3> Step 4: Fold face 6 downwards towards face 2 <image_4> Step 5: Fold face 1 inwards to...
B
{"initial_net": {"name": "1-3-2 Net", "faces": {"1": [[0.9999999999999999, 2.0, 1.0], [1.0, 0.9999999999999999, 1.0], [1.0, 1.0, 0.0], [0.9999999999999999, 2.0, 1.1102230246251565e-16]], "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": [[...
q+steps+all_for_valid_vis
[ "no", "yes" ]
53_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 1 Step 5: Fold face 1 downwards towards face 4 Based on the above ste...
A
{"initial_net": {"name": "Linear 6-Face Row", "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, 0.0, 0.0], [3.0, 0.0,...
q+steps
[ "no", "yes" ]
23_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 ...
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], [3.0000000...
q+steps+all_intermediate_vis
[ "no", "yes" ]
100_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 inwards towards face 2 <image_3> Step 4: Fold face 6 downwards towards face 2 <image_4> Based on the above steps, can ...
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....
q+steps+all_intermediate_vis
[ "yes", "no" ]
35_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 5 upwards <image_1> Step 2: Fold face 4 inwards towards face 1 <image_2> 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...
A
{"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...
q+steps+partial_vis
[ "yes", "no" ]
90_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 6 upwards <image_1> Step 2: Fold face 3 upwards towards face 6 <image_2> Step 3: Fold face 4 downwards towards face 6 Step 4: Fold face 5 downwards towards face 1 Step 5: Fold face 1 upwards towar...
B
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=1)", "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....
q+steps+partial_vis
[ "yes", "no" ]
33_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 3 upwards towards face 6 <image_2> Step 4: Fold face 4 upwards towards face 1 Step 5: Fold face 1 inwards towards face 4 Based on the above steps, can the net...
B
{"initial_net": {"name": "Net H: Two rows with bottom row shifted right", "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,...
q+steps+all_intermediate_vis
[ "yes", "no" ]
76_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 4 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 2 downwards towards face 1 <image_3> Step 4: Fold face 5 upwards towards face 2 <image_4> Step 5: Fold fa...
A
{"initial_net": {"name": "1-3-2 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, 1.0, 1.0], [2.0, 1.0, 1.0], [2.0, 0.0, 1.0000000000000002], [1.0, 0.0, 1.0000000000000002]], "3": [[1.0, 1.0, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [1.0,...
q+steps+all_for_valid_vis
[ "yes", "no" ]
89_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 downwards towards face 1 <image_3> Step 5: Fold face 6 downwards towards face 2 Based on the above steps, can the net ...
A
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=0)", "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....
q+steps+all_intermediate_vis
[ "no", "yes" ]
20_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 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 Step 5: Fold face 6 downw...
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],...
q+steps+partial_vis
[ "yes", "no" ]
100_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 <image_2> Step 3: Fold face 5 inwards towards face 2 <image_3> Step 4: Fold face 6 downwards towards face 2 Step 5: Fold face 1 inwards towards face...
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....
q+steps+partial_vis
[ "yes", "no" ]
70_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 inwards towards face 2 <image_3> Step 4: Fold face 6 downwards towards face 2 <image_4> Based on the above steps, can ...
A
{"initial_net": {"name": "1-3-2 Net", "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": [[1.0, 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....
q+steps+all_intermediate_vis
[ "yes", "no" ]
0_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 downwards Step 3: Fold face 3 downwards towards face 5 Step 4: Fold face 2 downwards towards face 4 Step 5: Fold face 1 upwards towards face 4 Based on the ...
B
{"initial_net": {"name": "3-3 Net", "faces": {"1": [[2.0, -2.0000000000000004, -1.1102230246251565e-16], [2.0, -2.0000000000000004, 0.9999999999999999], [2.0, -1.0000000000000004, 0.9999999999999998], [2.0, -1.0000000000000004, -1.1102230246251565e-16]], "2": [[0.9999999999999999, -2.0, 0.0], [1.0, -2.0, 1.0], [2.0, -2...
q+steps+partial_vis
[ "no", "yes" ]
113_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 3 Step 5: Fold face 1 downwards towards face 4 Based on the above steps, can the net be folde...
A
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=1)", "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...
q+steps+all_intermediate_vis
[ "no", "yes" ]
55_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 3: Fold face 5 upwards towards face 1 <image_3> Step 5: Fold face 1 downwards towards face 4 Based on the above steps, can the net ...
B
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=3)", "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...
q+steps+all_intermediate_vis
[ "yes", "no" ]
111_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 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 Step 5: Fold face 6 downw...
A
{"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], [...
q+steps+partial_vis
[ "yes", "no" ]
110_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 <image_3> Step 4: Fold face 2 downwards towards face 5 <image_4> Step 5: Fold ...
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...
q+steps+partial_vis
[ "yes", "no" ]
5_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 upwards towards face 1 Step 5: Fold face 6 downwards towards face 1 Based on the above ste...
B
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=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, 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....
q+steps
[ "yes", "no" ]
123_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 upwards towards face 1 Step 5: Fold face 6 downwards towards face 1 Based on the above ste...
B
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=2)", "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....
q+steps
[ "yes", "no" ]
75_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 2 Step 4: Fold face 6 inwards towards face 2 Step 5: Fold face 1 downwards towards face 3 Based...
B
{"initial_net": {"name": "1-3-2 Net", "faces": {"1": [[0.9999999999999999, 0.9999999999999998, 0.0], [1.0, 1.0, 1.0], [1.0, 0.0, 1.0000000000000002], [0.9999999999999999, -2.220446049250313e-16, 2.220446049250313e-16]], "2": [[1.0, 1.0, 1.0], [2.0, 1.0, 1.0], [2.0, 0.0, 1.0000000000000002], [1.0, 0.0, 1.000000000000000...
q+steps+partial_vis
[ "no", "yes" ]
38_q+steps
Check out a net with 6 faces below: <image_0>Below are the steps to fold the net with face 5 as the base: Step 1: Fold face 6 upwards Step 2: Fold face 3 upwards towards face 6 Step 3: Fold face 4 upwards towards face 3 Step 4: Fold face 2 downwards towards face 3 Step 5: Fold face 1 downwards towards face 4 Based on ...
B
{"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...
q+steps
[ "no", "yes" ]
119_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 2 upwards <image_1> Step 2: Fold face 4 inwards towards face 1 <image_2> Step 3: Fold face 3 downwards towards face 4 <image_3> Step 4: Fold face 5 inwards towards face 1 <image_4> Step 5: Fold fa...
A
{"initial_net": {"name": "Big T Net", "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": [[1.0, 0.0, 1.0], [0.0, 0.0, 1.0000000000000002], [0.0, 1.0, 1.0000000000000002], [1.0, 1.0, 1.0]], "4": [[0.0, -6.123233995736766e-17, 0.0],...
q+steps+all_for_valid_vis
[ "yes", "no" ]
134_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 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...
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....
q+steps
[ "no", "yes" ]
54_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 <image_2> Step 3: Fold face 5 downwards towards face 2 Step 4: Fold face 6 downwards towards face 2 Step 5: Fold face 1 inwards towards face 3 Based...
B
{"initial_net": {"name": "invalid_G", "faces": {"2": [[0.9999999999999999, 0.0, 1.0], [1.0, 0.0, 0.0], [1.0, 1.0, 0.0], [0.9999999999999999, 1.0, 1.0]], "3": [[1, 0, 0], [2, 0, 0], [2, 1, 0], [1, 1, 0]], "4": [[2.0, 0.0, 0.0], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [2.0, 1.0, 0.0]], "5": [[2.0, 0.0, 1.0], [1.0, 0.0, 1.0], [...
q+steps+partial_vis
[ "yes", "no" ]
58_q_only
Check out a net with 6 faces below: <image_0>Can the net be folded to form a cube, yes or no?
A
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=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....
q_only
[ "no", "yes" ]
47_q+steps
Check out a net with 6 faces below: <image_0>Below are the steps to fold the net with face 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 downwards towards face 2 Step 5: Fold face 1 downwards towards face 3 Based on ...
B
{"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, -0.9999999...
q+steps
[ "no", "yes" ]
99_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 inwards towards face 3 Step 3: Fold face 5 upwards towards face 2 Step 4: Fold face 6 upwards towards face 3 Step 5: Fold face 1 downwards towards face 4 Based on th...
B
{"initial_net": {"name": "Net H: Two rows with bottom row shifted right", "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": ...
q+steps
[ "yes", "no" ]
139_q+steps
Check out a net with 6 faces below: <image_0>Below are the steps to fold the net with face 5 as the base: Step 1: Fold face 6 upwards Step 2: Fold face 3 upwards towards face 6 Step 3: Fold face 2 inwards towards face 5 Step 4: Fold face 4 inwards towards face 1 Step 5: Fold face 1 inwards towards face 4 Based on the ...
A
{"initial_net": {"name": "invalid_F", "faces": {"1": [[3.0, -2.83276944882399e-16, 0.0], [2.0, 0.0, 0.0], [2.0, 0.0, 1.0], [3.0, -2.83276944882399e-16, 1.0]], "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": [[2.0,...
q+steps
[ "no", "yes" ]
93_q+steps
Check out a net with 6 faces below: <image_0>Below are the steps to fold the net with face 3 as the base: Step 1: Fold face 6 upwards Step 2: Fold face 2 upwards towards face 6 Step 3: Fold face 4 upwards towards face 6 Step 4: Fold face 5 downwards towards face 1 Step 5: Fold face 1 downwards towards face 4 Based on ...
A
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=2)", "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....
q+steps
[ "no", "yes" ]
19_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 3: Fold face 5 upwards towards face 2 <image_3> Step 4: Fold face 6 inwards towards face 2 <image_4> Based on the above steps, can ...
A
{"initial_net": {"name": "t-shaped Net", "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]], "1": [[0.9999999999999999, 1.0, 1.0], [1.0, 1.0, 0.0], [2.0, 1.0, 1.1102230246251565e-16], [2.0, 1.0, 1.0]], "2": [[2.0, 0.0, 1.0], [0.9999999999999999, 0.0, 1.0], ...
q+steps+all_intermediate_vis
[ "yes", "no" ]
121_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 2 Step 4: Fold face 6 inwards towards face 1 Step 5: Fold face 1 downwards towards face 6 Based...
A
{"initial_net": {"name": "invalid_E", "faces": {"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]], "6": [[3.0, 1.0, 0.0], [3.0, 1.0, 1.0], [2.0, 1.0, 1.0], [2.0, 1.0, 0.0]], "2": [[3.0, 0.0, 1.0000000000000002], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [3.0, 1.0, 1.0000...
q+steps+partial_vis
[ "no", "yes" ]
64_q_only
Check out a net with 6 faces below: <image_0>Can the net be folded to form a cube, yes or no?
A
{"initial_net": {"name": "invalid_E", "faces": {"1": [[0.9999999999999999, 1.0, 1.0], [1.0, 1.0, 0.0], [2.0, 1.0, 1.1102230246251565e-16], [2.0, 1.0, 1.0]], "6": [[2.0, 1.0, 1.0], [1.0, 1.0, 1.0], [1.0, 1.0, 0.0], [2.0, 1.0, 0.0]], "2": [[0.9999999999999999, 0.0, 1.0], [1.0, 0.0, 0.0], [1.0, 1.0, 0.0], [0.9999999999999...
q_only
[ "no", "yes" ]
30_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 2 upwards <image_1> Step 2: Fold face 3 inwards towards face 1 Step 3: Fold face 4 inwards towards face 1 Step 4: Fold face 5 downwards towards face 2 Step 5: Fold face 6 downwards towards face 1 ...
A
{"initial_net": {"name": "1-3-2 Net", "faces": {"1": [[0, 2, 0], [1, 2, 0], [1, 3, 0], [0, 3, 0]], "2": [[1.0, 2.0, 0.0], [1.0, 2.0, 1.0], [1.0, 3.0, 1.0], [1.0, 3.0, 0.0]], "3": [[0.0, 2.0, 0.0], [0.0, 2.0, 1.0], [1.0, 2.0, 1.0], [1.0, 2.0, 0.0]], "4": [[-2.83276944882399e-16, 3.0, 0.0], [-2.83276944882399e-16, 3.0, 1...
q+steps+partial_vis
[ "yes", "no" ]
98_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 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> Based on the above steps, can ...
A
{"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....
q+steps+all_intermediate_vis
[ "yes", "no" ]
60_q+steps
Check out a net with 6 faces below: <image_0>Below are the steps to fold the net with face 1 as the base: Step 1: Fold face 2 upwards Step 2: Fold face 4 inwards towards face 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 for...
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, 1.0000000000...
q+steps
[ "no", "yes" ]
141_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 3 upwards <image_1> Step 2: Fold face 2 inwards towards face 6 <image_2> Step 3: Fold face 4 inwards towards face 6 Step 4: Fold face 5 downwards towards face 2 Step 5: Fold face 1 downwards towar...
A
{"initial_net": {"name": "t-shaped Net Variant 1", "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, -0.9999999...
q+steps+partial_vis
[ "yes", "no" ]
82_q+steps
Check out a net with 6 faces below: <image_0>Below are the steps to fold the net with face 4 as the base: Step 1: Fold face 1 upwards Step 2: Fold face 3 upwards towards face 1 Step 3: Fold face 2 downwards towards face 1 Step 4: Fold face 5 upwards towards face 2 Step 5: Fold face 6 inwards towards face 2 Based on th...
A
{"initial_net": {"name": "t-shaped Net Variant 1", "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]]...
q+steps
[ "yes", "no" ]
9_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 towards face 1 Step 3: Fold face 4 inwards towards face 2 Step 4: Fold face 5 downwards towards face 1 Step 5: Fold face 6 downwards towards face 1 Based on ...
A
{"initial_net": {"name": "2-2 net", "faces": {"1": [[0.0, 3.0, 0.0], [1.0, 3.0, 0.0], [1.0, 3.0, 1.0], [0.0, 3.0, 1.0]], "2": [[0, 2, 0], [1, 2, 0], [1, 3, 0], [0, 3, 0]], "3": [[1.0, 2.0, 0.0], [1.0, 2.0, 1.0], [1.0, 3.0, 1.0], [1.0, 3.0, 0.0]], "4": [[0.0, 2.0, 0.0], [0.0, 2.0, 1.0], [1.0, 2.0, 1.0], [1.0, 2.0, 0.0]]...
q+steps
[ "yes", "no" ]
133_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 Step 3: Fold face 4 downwards towards face 1 Step 4: Fold face 5 downwards towards face 2 Step 5: Fold face 6 inwards towards face 1 ...
B
{"initial_net": {"name": "1-3-2 Net", "faces": {"1": [[0.9999999999999999, 2.0, 1.0], [1.0, 2.0, 0.0], [1.0, 3.0, 0.0], [0.9999999999999999, 3.0, 1.0]], "2": [[1, 2, 0], [2, 2, 0], [2, 3, 0], [1, 3, 0]], "3": [[1.0, 2.0, 1.0], [2.0, 2.0, 1.0], [2.0, 2.0, 0.0], [1.0, 2.0, 0.0]], "4": [[1.0, 3.0, 1.0000000000000002], [2....
q+steps+partial_vis
[ "no", "yes" ]
95_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 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 inwards towards face 1 <image_4> Step 5: Fold face...
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-1...
q+steps+all_for_valid_vis
[ "no", "yes" ]
92_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 inwards towards face 4 <image_2> Step 3: Fold face 5 upwards towards face 3 <image_3> Step 4: Fold face 6 inwards towards face 2 Step 5: Fold face 1 downwar...
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":...
q+steps+partial_vis
[ "no", "yes" ]
5_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 downwards towards face 1 Based on the above steps, can the net be folded ...
A
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=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, 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....
q+steps+all_intermediate_vis
[ "no", "yes" ]
129_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 3: Fold face 2 downwards towards face 5 Step 4: Fold face 4 upwards towards face 2 Step 5: Fold face 1 downwards towards face 5 Based on the above steps, can the net be fo...
A
{"initial_net": {"name": "invalid_F", "faces": {"1": [[3.0, -2.83276944882399e-16, 0.0], [3.0, 0.0, 1.0], [4.0, 0.0, 1.0], [4.0, -2.83276944882399e-16, 0.0]], "2": [[3.0, 0.0, 1.0], [3.0, 1.0, 1.0], [4.0, 1.0, 1.0], [4.0, 0.0, 1.0]], "3": [[3.0, 1.0, 1.0], [3.0, 1.0, 0.0], [4.0, 1.0, 0.0], [4.0, 1.0, 1.0]], "4": [[3.0,...
q+steps+all_intermediate_vis
[ "no", "yes" ]
107_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 inwards towards face 6 Step 4: Fold face 2 inwards towards face 6 Step 5: Fold face 1 upwards towards f...
B
{"initial_net": {"name": "invalid_E", "faces": {"1": [[4.0, 1.0, 3.3306690738754696e-16], [4.0, 2.0, 2.220446049250313e-16], [3.0, 2.0, 1.6081226496766364e-16], [3.0, 1.0, -6.163438522699459e-16]], "6": [[3, 1, 0], [4, 1, 0], [4, 2, 0], [3, 2, 0]], "2": [[4.0, 1.0, 1.0000000000000004], [4.0, 2.0, 1.0000000000000002], [...
q+steps+partial_vis
[ "yes", "no" ]
8_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 4 upwards towards face 6 Step 3: Fold face 3 inwards towards face 5 Step 4: Fold face 2 inwards towards face 5 Step 5: Fold face 1 downwards towards face 3 Ba...
B
{"initial_net": {"name": "1-3-2 Net", "faces": {"1": [[2.0, 0.9999999999999996, 1.0], [3.0, 1.0, 1.0], [3.0000000000000004, 0.0, 1.0], [2.0000000000000004, -4.440892098500626e-16, 1.0]], "2": [[3.0, 1.0, 1.0], [3.0, 1.0, 0.0], [3.0000000000000004, 0.0, 0.0], [3.0000000000000004, 0.0, 1.0]], "3": [[2.0, 1.0, 1.0], [2.0,...
q+steps+partial_vis
[ "no", "yes" ]
69_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 3 upwards <image_1> Step 2: Fold face 6 inwards towards face 2 <image_2> Step 3: Fold face 4 downwards towards face 6 <image_3> Step 4: Fold face 5 downwards towards face 2 <image_4> Based on the ...
B
{"initial_net": {"name": "t-shaped Net Variant 2", "faces": {"3": [[0.0, 0.0, 0.0], [6.123233995736766e-17, 0.0, 1.0], [6.123233995736766e-17, 1.0, 1.0], [0.0, 1.0, 0.0]], "2": [[-1, 0, 0], [0, 0, 0], [0, 1, 0], [-1, 1, 0]], "4": [[6.123233995736766e-17, 0.0, 1.0], [-0.9999999999999999, 0.0, 1.0000000000000002], [-0.99...
q+steps+all_intermediate_vis
[ "no", "yes" ]
2_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 3 downwards towards face 5 <image_3> Step 4: Fold face 2 downwards towards face 3 <image_4> Step 5: Fold face 1 downwa...
B
{"initial_net": {"name": "Big T - Variant 1", "faces": {"1": [[0.9999999999999999, -2.0, 0.9999999999999998], [1.0, -3.0, 1.0000000000000002], [1.0, -3.0000000000000004, 2.220446049250313e-16], [0.9999999999999999, -2.0000000000000004, -2.220446049250313e-16]], "2": [[1.0, -3.0, 1.0000000000000002], [2.0, -3.0, 1.00000...
q+steps+all_for_valid_vis
[ "no", "yes" ]