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Graphics3D[GraphicsComplex[{{-1/2, -1/2, -1/2 - 1/Sqrt[2]}, {-1/2, -1/2, 1/2 + 1/Sqrt[2]},
   {-1/2, 1/2, -1/2 - 1/Sqrt[2]}, {-1/2, 1/2, 1/2 + 1/Sqrt[2]}, {-1/2, -1/2 - 1/Sqrt[2], -1/2},
   {-1/2, -1/2 - 1/Sqrt[2], 1/2}, {-1/2, 1/2 + 1/Sqrt[2], -1/2}, {-1/2, 1/2 + 1/Sqrt[2], 1/2},
   {1/2, -1/2, -1/2 - 1/Sqrt[2]}, {1/2, -1/2, 1/2 + 1/Sqrt[2]}, {1/2, 1/2, -1/2 - 1/Sqrt[2]},
   {1/2, 1/2, 1/2 + 1/Sqrt[2]}, {1/2, -1/2 - 1/Sqrt[2], -1/2}, {1/2, -1/2 - 1/Sqrt[2], 1/2},
   {1/2, 1/2 + 1/Sqrt[2], -1/2}, {1/2, 1/2 + 1/Sqrt[2], 1/2}, {-1/2 - 1/Sqrt[2], -1/2, -1/2},
   {-1/2 - 1/Sqrt[2], -1/2, 1/2}, {-1/2 - 1/Sqrt[2], 1/2, -1/2}, {-1/2 - 1/Sqrt[2], 1/2, 1/2},
   {1/2 + 1/Sqrt[2], -1/2, -1/2}, {1/2 + 1/Sqrt[2], -1/2, 1/2}, {1/2 + 1/Sqrt[2], 1/2, -1/2},
   {1/2 + 1/Sqrt[2], 1/2, 1/2}}, Polygon[{{3, 11, 9, 1}, {2, 10, 12, 4}, {24, 22, 21, 23},
    {19, 17, 18, 20}, {5, 13, 14, 6}, {8, 16, 15, 7}, {13, 21, 22, 14}, {16, 24, 23, 15},
    {6, 18, 17, 5}, {7, 19, 20, 8}, {6, 14, 10, 2}, {4, 12, 16, 8}, {22, 24, 12, 10},
    {2, 4, 20, 18}, {1, 9, 13, 5}, {7, 15, 11, 3}, {9, 11, 23, 21}, {17, 19, 3, 1}, {22, 10, 14},
    {16, 12, 24}, {6, 2, 18}, {20, 4, 8}, {13, 9, 21}, {23, 11, 15}, {17, 1, 5}, {7, 3, 19}}]]]

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Archimedean Solid

Geometry