Hellenica World

Parabiaugmented dodecahedron

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Graphics3D[GraphicsComplex[{{0, 0, Root[9 - 36*#1^2 + 16*#1^4 & , 4, 0]},
   {0, 0, Root[9 - 36*#1^2 + 16*#1^4 & , 1, 0]}, {Root[1 - 36*#1^2 + 144*#1^4 & , 3, 0], (-3 - Sqrt[5])/4,
    Root[1 - 36*#1^2 + 144*#1^4 & , 4, 0]}, {Root[1 - 36*#1^2 + 144*#1^4 & , 3, 0], (3 + Sqrt[5])/4,
    Root[1 - 36*#1^2 + 144*#1^4 & , 4, 0]}, {Root[1 - 36*#1^2 + 144*#1^4 & , 4, 0], (-1 - Sqrt[5])/4,
    Root[25 - 180*#1^2 + 144*#1^4 & , 1, 0]}, {Root[1 - 36*#1^2 + 144*#1^4 & , 4, 0], (1 + Sqrt[5])/4,
    Root[25 - 180*#1^2 + 144*#1^4 & , 1, 0]}, {Root[25 - 180*#1^2 + 144*#1^4 & , 4, 0], (-1 - Sqrt[5])/4,
    Root[1 - 36*#1^2 + 144*#1^4 & , 4, 0]}, {Root[25 - 180*#1^2 + 144*#1^4 & , 4, 0], (1 + Sqrt[5])/4,
    Root[1 - 36*#1^2 + 144*#1^4 & , 4, 0]}, {Root[1 - 216*#1^2 + 144*#1^4 & , 1, 0], -1/2,
    Root[1 - 36*#1^2 + 144*#1^4 & , 4, 0]}, {Root[1 - 216*#1^2 + 144*#1^4 & , 1, 0], 1/2,
    Root[1 - 36*#1^2 + 144*#1^4 & , 4, 0]}, {Root[1 - 216*#1^2 + 144*#1^4 & , 4, 0], -1/2,
    Root[1 - 36*#1^2 + 144*#1^4 & , 1, 0]}, {Root[1 - 216*#1^2 + 144*#1^4 & , 4, 0], 1/2,
    Root[1 - 36*#1^2 + 144*#1^4 & , 1, 0]}, {Root[1 - 9*#1^2 + 9*#1^4 & , 1, 0], 0,
    Root[25 - 180*#1^2 + 144*#1^4 & , 1, 0]}, {Root[1 - 36*#1^2 + 144*#1^4 & , 1, 0], (-1 - Sqrt[5])/4,
    Root[25 - 180*#1^2 + 144*#1^4 & , 4, 0]}, {Root[1 - 36*#1^2 + 144*#1^4 & , 1, 0], (1 + Sqrt[5])/4,
    Root[25 - 180*#1^2 + 144*#1^4 & , 4, 0]}, {Root[1 - 9*#1^2 + 9*#1^4 & , 4, 0], 0,
    Root[25 - 180*#1^2 + 144*#1^4 & , 4, 0]}, {Root[25 - 180*#1^2 + 144*#1^4 & , 1, 0], (-1 - Sqrt[5])/4,
    Root[1 - 36*#1^2 + 144*#1^4 & , 1, 0]}, {Root[25 - 180*#1^2 + 144*#1^4 & , 1, 0], (1 + Sqrt[5])/4,
    Root[1 - 36*#1^2 + 144*#1^4 & , 1, 0]}, {Root[121 - 345*#1^2 + 225*#1^4 & , 4, 0], 0,
    Root[121 - 6180*#1^2 + 3600*#1^4 & , 1, 0]}, {Root[121 - 345*#1^2 + 225*#1^4 & , 1, 0], 0,
    Root[121 - 6180*#1^2 + 3600*#1^4 & , 4, 0]}, {Root[1 - 36*#1^2 + 144*#1^4 & , 2, 0], (-3 - Sqrt[5])/4,
    Root[1 - 36*#1^2 + 144*#1^4 & , 1, 0]}, {Root[1 - 36*#1^2 + 144*#1^4 & , 2, 0], (3 + Sqrt[5])/4,
    Root[1 - 36*#1^2 + 144*#1^4 & , 1, 0]}}, Polygon[{{5, 11, 7, 3, 21}, {11, 12, 8, 16, 7},
    {12, 6, 22, 4, 8}, {6, 2, 13, 18, 22}, {2, 5, 21, 17, 13}, {4, 22, 18, 10, 15}, {18, 13, 17, 9, 10},
    {17, 21, 3, 14, 9}, {3, 7, 16, 1, 14}, {16, 8, 4, 15, 1}, {20, 15, 10}, {20, 10, 9}, {20, 9, 14},
    {20, 14, 1}, {20, 1, 15}, {19, 2, 6}, {19, 6, 12}, {19, 12, 11}, {19, 11, 5}, {19, 5, 2}}]]]

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Johnson Polyhedra

Geometry