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Graphics3D[GraphicsComplex[{{-3/2, -1/2, 0}, {-3/2, 1/2, 0}, {-1, -1, -(1/Sqrt[2])},
   {-1, -1, 1/Sqrt[2]}, {-1, 1, -(1/Sqrt[2])}, {-1, 1, 1/Sqrt[2]}, {-1/2, -3/2, 0},
   {-1/2, -1/2, -Sqrt[2]}, {-1/2, -1/2, Sqrt[2]}, {-1/2, 1/2, -Sqrt[2]}, {-1/2, 1/2, Sqrt[2]},
   {-1/2, 3/2, 0}, {1/2, -3/2, 0}, {1/2, -1/2, -Sqrt[2]}, {1/2, -1/2, Sqrt[2]},
   {1/2, 1/2, -Sqrt[2]}, {1/2, 1/2, Sqrt[2]}, {1/2, 3/2, 0}, {1, -1, -(1/Sqrt[2])},
   {1, -1, 1/Sqrt[2]}, {1, 1, -(1/Sqrt[2])}, {1, 1, 1/Sqrt[2]}, {3/2, -1/2, 0}, {3/2, 1/2, 0}},
  Polygon[{{17, 11, 9, 15}, {14, 8, 10, 16}, {22, 24, 21, 18}, {12, 5, 2, 6}, {13, 19, 23, 20},
    {4, 1, 3, 7}, {19, 13, 7, 3, 8, 14}, {15, 9, 4, 7, 13, 20}, {16, 10, 5, 12, 18, 21},
    {22, 18, 12, 6, 11, 17}, {20, 23, 24, 22, 17, 15}, {14, 16, 21, 24, 23, 19},
    {9, 11, 6, 2, 1, 4}, {3, 1, 2, 5, 10, 8}}]]]

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Archimedean Solid

Geometry