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Graphics3D[GraphicsComplex[{{-1/2, (1 + Sqrt[2])/2, (1 + Sqrt[2])/2},
   {-1/2, (1 + Sqrt[2])/2, (-1 - Sqrt[2])/2}, {-1/2, (-1 - Sqrt[2])/2, (1 + Sqrt[2])/2},
   {-1/2, (-1 - Sqrt[2])/2, (-1 - Sqrt[2])/2}, {0, -(1/Sqrt[2]), (1 + 2*Sqrt[2])/2},
   {0, -(1/Sqrt[2]), (-1 - 2*Sqrt[2])/2}, {0, 1/Sqrt[2], (1 + 2*Sqrt[2])/2},
   {0, 1/Sqrt[2], (-1 - 2*Sqrt[2])/2}, {1/2, (1 + Sqrt[2])/2, (1 + Sqrt[2])/2},
   {1/2, (1 + Sqrt[2])/2, (-1 - Sqrt[2])/2}, {1/2, (-1 - Sqrt[2])/2, (1 + Sqrt[2])/2},
   {1/2, (-1 - Sqrt[2])/2, (-1 - Sqrt[2])/2}, {-(1/Sqrt[2]), 0, (1 + 2*Sqrt[2])/2},
   {-(1/Sqrt[2]), 0, (-1 - 2*Sqrt[2])/2}, {1/Sqrt[2], 0, (1 + 2*Sqrt[2])/2},
   {1/Sqrt[2], 0, (-1 - 2*Sqrt[2])/2}, {(1 + Sqrt[2])/2, -1/2, (1 + Sqrt[2])/2},
   {(1 + Sqrt[2])/2, -1/2, (-1 - Sqrt[2])/2}, {(1 + Sqrt[2])/2, 1/2, (1 + Sqrt[2])/2},
   {(1 + Sqrt[2])/2, 1/2, (-1 - Sqrt[2])/2}, {(1 + Sqrt[2])/2, (1 + Sqrt[2])/2, -1/2},
   {(1 + Sqrt[2])/2, (1 + Sqrt[2])/2, 1/2}, {(1 + Sqrt[2])/2, (-1 - Sqrt[2])/2, -1/2},
   {(1 + Sqrt[2])/2, (-1 - Sqrt[2])/2, 1/2}, {(-1 - Sqrt[2])/2, -1/2, (1 + Sqrt[2])/2},
   {(-1 - Sqrt[2])/2, -1/2, (-1 - Sqrt[2])/2}, {(-1 - Sqrt[2])/2, 1/2, (1 + Sqrt[2])/2},
   {(-1 - Sqrt[2])/2, 1/2, (-1 - Sqrt[2])/2}, {(-1 - Sqrt[2])/2, (1 + Sqrt[2])/2, -1/2},
   {(-1 - Sqrt[2])/2, (1 + Sqrt[2])/2, 1/2}, {(-1 - Sqrt[2])/2, (-1 - Sqrt[2])/2, -1/2},
   {(-1 - Sqrt[2])/2, (-1 - Sqrt[2])/2, 1/2}},
  Polygon[{{3, 32, 31, 4, 12, 23, 24, 11}, {9, 22, 21, 10, 2, 29, 30, 1},
    {17, 24, 23, 18, 20, 21, 22, 19}, {27, 30, 29, 28, 26, 31, 32, 25}, {24, 17, 11},
    {9, 19, 22}, {3, 25, 32}, {30, 27, 1}, {12, 18, 23}, {21, 20, 10}, {31, 26, 4}, {2, 28, 29},
    {16, 6, 14, 8}, {28, 2, 8, 14}, {4, 26, 14, 6}, {18, 12, 6, 16}, {10, 20, 16, 8},
    {8, 2, 10}, {14, 26, 28}, {6, 12, 4}, {16, 20, 18}, {7, 13, 5, 15}, {13, 7, 1, 27},
    {5, 13, 25, 3}, {15, 5, 11, 17}, {7, 15, 19, 9}, {9, 1, 7}, {27, 25, 13}, {3, 11, 5},
    {17, 19, 15}}]]]

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