Hellenica World

Square orthobicupola

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Graphics3D[GraphicsComplex[{{0, -(1/Sqrt[2]), -(1/Sqrt[2])}, {0, -(1/Sqrt[2]), 1/Sqrt[2]},
   {0, 1/Sqrt[2], -(1/Sqrt[2])}, {0, 1/Sqrt[2], 1/Sqrt[2]}, {-(1/Sqrt[2]), 0, -(1/Sqrt[2])},
   {-(1/Sqrt[2]), 0, 1/Sqrt[2]}, {1/Sqrt[2], 0, -(1/Sqrt[2])}, {1/Sqrt[2], 0, 1/Sqrt[2]},
   {1/2, (1 + Sqrt[2])/2, 0}, {-1/2, (1 + Sqrt[2])/2, 0}, {(-1 - Sqrt[2])/2, 1/2, 0},
   {(-1 - Sqrt[2])/2, -1/2, 0}, {-1/2, (-1 - Sqrt[2])/2, 0}, {1/2, (-1 - Sqrt[2])/2, 0},
   {(1 + Sqrt[2])/2, -1/2, 0}, {(1 + Sqrt[2])/2, 1/2, 0}},
  Polygon[{{4, 6, 2, 8}, {6, 4, 10, 11}, {2, 6, 12, 13}, {8, 2, 14, 15}, {4, 8, 16, 9},
    {9, 10, 4}, {11, 12, 6}, {13, 14, 2}, {15, 16, 8}, {7, 1, 5, 3}, {11, 10, 3, 5},
    {13, 12, 5, 1}, {15, 14, 1, 7}, {9, 16, 7, 3}, {3, 10, 9}, {5, 12, 11}, {1, 14, 13},
    {7, 16, 15}}]]]

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Johnson Polyhedra

Geometry