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

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Archimedean Solid

Geometry