Hellenica World

Pentagonal orthobirotunda

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

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Johnson Polyhedra

Geometry