Hellenica World

# Gyroelongated square pyramid

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Graphics3D[GraphicsComplex[{{-1/2, -1/2, (20 - 27*Sqrt[2] - 2*Sqrt[-168 + 121*Sqrt[2]])/184 -
Sqrt[4 - Sec[Pi/8]^2]/4}, {-1/2, 1/2, (20 - 27*Sqrt[2] - 2*Sqrt[-168 + 121*Sqrt[2]])/184 -
Sqrt[4 - Sec[Pi/8]^2]/4}, {0, 0, 1/Sqrt[2] + (20 - 27*Sqrt[2] - 2*Sqrt[-168 + 121*Sqrt[2]])/184 +
Sqrt[4 - Sec[Pi/8]^2]/4}, {0, -(1/Sqrt[2]), (20 - 27*Sqrt[2] - 2*Sqrt[-168 + 121*Sqrt[2]])/184 +
Sqrt[4 - Sec[Pi/8]^2]/4}, {0, 1/Sqrt[2], (20 - 27*Sqrt[2] - 2*Sqrt[-168 + 121*Sqrt[2]])/184 +
Sqrt[4 - Sec[Pi/8]^2]/4}, {1/2, -1/2, (20 - 27*Sqrt[2] - 2*Sqrt[-168 + 121*Sqrt[2]])/184 -
Sqrt[4 - Sec[Pi/8]^2]/4}, {1/2, 1/2, (20 - 27*Sqrt[2] - 2*Sqrt[-168 + 121*Sqrt[2]])/184 -
Sqrt[4 - Sec[Pi/8]^2]/4}, {-(1/Sqrt[2]), 0, (20 - 27*Sqrt[2] - 2*Sqrt[-168 + 121*Sqrt[2]])/184 +
Sqrt[4 - Sec[Pi/8]^2]/4}, {1/Sqrt[2], 0, (20 - 27*Sqrt[2] - 2*Sqrt[-168 + 121*Sqrt[2]])/184 +
Sqrt[4 - Sec[Pi/8]^2]/4}}, Polygon[{{6, 1, 2, 7}, {7, 5, 9}, {2, 8, 5}, {1, 4, 8}, {6, 9, 4}, {7, 2, 5},
{2, 1, 8}, {1, 6, 4}, {6, 7, 9}, {5, 8, 3}, {8, 4, 3}, {4, 9, 3}, {9, 5, 3}}]]]

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Johnson Polyhedra

Geometry