Hellenica World

Triaugmented dodecahedron

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Graphics3D[GraphicsComplex[{{-Sqrt[(7 - 3*Sqrt[5])/30]/6, 0, -Sqrt[(7 - 3*Sqrt[5])/6]/12 +
     Root[9 - 36*#1^2 + 16*#1^4 & , 4, 0]}, {-Sqrt[(7 - 3*Sqrt[5])/30]/6, 0,
    -Sqrt[(7 - 3*Sqrt[5])/6]/12 + Root[9 - 36*#1^2 + 16*#1^4 & , 1, 0]},
   {-Sqrt[(7 - 3*Sqrt[5])/30]/6 + Root[1 - 36*#1^2 + 144*#1^4 & , 3, 0], (-3 - Sqrt[5])/4,
    -Sqrt[(7 - 3*Sqrt[5])/6]/12 + Root[1 - 36*#1^2 + 144*#1^4 & , 4, 0]},
   {-Sqrt[(7 - 3*Sqrt[5])/30]/6 + Root[1 - 36*#1^2 + 144*#1^4 & , 3, 0], (3 + Sqrt[5])/4,
    -Sqrt[(7 - 3*Sqrt[5])/6]/12 + Root[1 - 36*#1^2 + 144*#1^4 & , 4, 0]},
   {-Sqrt[(7 - 3*Sqrt[5])/30]/6 + Root[1 - 36*#1^2 + 144*#1^4 & , 4, 0], (-1 - Sqrt[5])/4,
    -Sqrt[(7 - 3*Sqrt[5])/6]/12 + Root[25 - 180*#1^2 + 144*#1^4 & , 1, 0]},
   {-Sqrt[(7 - 3*Sqrt[5])/30]/6 + Root[1 - 36*#1^2 + 144*#1^4 & , 4, 0], (1 + Sqrt[5])/4,
    -Sqrt[(7 - 3*Sqrt[5])/6]/12 + Root[25 - 180*#1^2 + 144*#1^4 & , 1, 0]},
   {-Sqrt[(7 - 3*Sqrt[5])/30]/6 + Root[25 - 180*#1^2 + 144*#1^4 & , 4, 0], (-1 - Sqrt[5])/4,
    -Sqrt[(7 - 3*Sqrt[5])/6]/12 + Root[1 - 36*#1^2 + 144*#1^4 & , 4, 0]},
   {-Sqrt[(7 - 3*Sqrt[5])/30]/6 + Root[25 - 180*#1^2 + 144*#1^4 & , 4, 0], (1 + Sqrt[5])/4,
    -Sqrt[(7 - 3*Sqrt[5])/6]/12 + Root[1 - 36*#1^2 + 144*#1^4 & , 4, 0]},
   {-Sqrt[(7 - 3*Sqrt[5])/30]/6 + Root[1 - 216*#1^2 + 144*#1^4 & , 1, 0], -1/2,
    -Sqrt[(7 - 3*Sqrt[5])/6]/12 + Root[1 - 36*#1^2 + 144*#1^4 & , 4, 0]},
   {-Sqrt[(7 - 3*Sqrt[5])/30]/6 + Root[1 - 216*#1^2 + 144*#1^4 & , 1, 0], 1/2,
    -Sqrt[(7 - 3*Sqrt[5])/6]/12 + Root[1 - 36*#1^2 + 144*#1^4 & , 4, 0]},
   {-Sqrt[(7 - 3*Sqrt[5])/30]/6 + Root[1 - 216*#1^2 + 144*#1^4 & , 4, 0], -1/2,
    -Sqrt[(7 - 3*Sqrt[5])/6]/12 + Root[1 - 36*#1^2 + 144*#1^4 & , 1, 0]},
   {-Sqrt[(7 - 3*Sqrt[5])/30]/6 + Root[1 - 216*#1^2 + 144*#1^4 & , 4, 0], 1/2,
    -Sqrt[(7 - 3*Sqrt[5])/6]/12 + Root[1 - 36*#1^2 + 144*#1^4 & , 1, 0]},
   {-Sqrt[(7 - 3*Sqrt[5])/30]/6 + Root[1 - 9*#1^2 + 9*#1^4 & , 1, 0], 0,
    -Sqrt[(7 - 3*Sqrt[5])/6]/12 + Root[25 - 180*#1^2 + 144*#1^4 & , 1, 0]},
   {-Sqrt[(7 - 3*Sqrt[5])/30]/6 + Root[1 - 36*#1^2 + 144*#1^4 & , 1, 0], (-1 - Sqrt[5])/4,
    -Sqrt[(7 - 3*Sqrt[5])/6]/12 + Root[25 - 180*#1^2 + 144*#1^4 & , 4, 0]},
   {-Sqrt[(7 - 3*Sqrt[5])/30]/6 + Root[1 - 36*#1^2 + 144*#1^4 & , 1, 0], (1 + Sqrt[5])/4,
    -Sqrt[(7 - 3*Sqrt[5])/6]/12 + Root[25 - 180*#1^2 + 144*#1^4 & , 4, 0]},
   {-Sqrt[(7 - 3*Sqrt[5])/30]/6 + Root[1 - 9*#1^2 + 9*#1^4 & , 4, 0], 0,
    -Sqrt[(7 - 3*Sqrt[5])/6]/12 + Root[25 - 180*#1^2 + 144*#1^4 & , 4, 0]},
   {-Sqrt[(7 - 3*Sqrt[5])/30]/6 + Root[25 - 180*#1^2 + 144*#1^4 & , 1, 0], (-1 - Sqrt[5])/4,
    -Sqrt[(7 - 3*Sqrt[5])/6]/12 + Root[1 - 36*#1^2 + 144*#1^4 & , 1, 0]},
   {-Sqrt[(7 - 3*Sqrt[5])/30]/6 + Root[25 - 180*#1^2 + 144*#1^4 & , 1, 0], (1 + Sqrt[5])/4,
    -Sqrt[(7 - 3*Sqrt[5])/6]/12 + Root[1 - 36*#1^2 + 144*#1^4 & , 1, 0]},
   {-Sqrt[(7 - 3*Sqrt[5])/30]/6 + Root[121 - 345*#1^2 + 225*#1^4 & , 1, 0], 0,
    -Sqrt[(7 - 3*Sqrt[5])/6]/12 + Root[121 - 6180*#1^2 + 3600*#1^4 & , 4, 0]},
   {-Sqrt[(7 - 3*Sqrt[5])/30]/6 + Root[1 - 36*#1^2 + 144*#1^4 & , 2, 0], (-3 - Sqrt[5])/4,
    -Sqrt[(7 - 3*Sqrt[5])/6]/12 + Root[1 - 36*#1^2 + 144*#1^4 & , 1, 0]},
   {-Sqrt[(7 - 3*Sqrt[5])/30]/6 + Root[1 - 36*#1^2 + 144*#1^4 & , 2, 0], (3 + Sqrt[5])/4,
    -Sqrt[(7 - 3*Sqrt[5])/6]/12 + Root[1 - 36*#1^2 + 144*#1^4 & , 1, 0]},
   {-Sqrt[(7 - 3*Sqrt[5])/30]/6 + Root[121 - 2520*#1^2 + 3600*#1^4 & , 4, 0], (5 + 4*Sqrt[5])/10,
    -Sqrt[(7 - 3*Sqrt[5])/6]/12 + Root[121 - 1620*#1^2 + 3600*#1^4 & , 2, 0]},
   {-Sqrt[(7 - 3*Sqrt[5])/30]/6 + Root[121 - 2520*#1^2 + 3600*#1^4 & , 4, 0], (-5 - 4*Sqrt[5])/10,
    -Sqrt[(7 - 3*Sqrt[5])/6]/12 + Root[121 - 1620*#1^2 + 3600*#1^4 & , 2, 0]}},
  Polygon[{{2, 6, 12, 11, 5}, {11, 12, 8, 16, 7}, {6, 2, 13, 18, 21}, {2, 5, 20, 17, 13},
    {4, 21, 18, 10, 15}, {18, 13, 17, 9, 10}, {17, 20, 3, 14, 9}, {3, 7, 16, 1, 14}, {16, 8, 4, 15, 1},
    {19, 15, 10}, {19, 10, 9}, {19, 9, 14}, {19, 14, 1}, {19, 1, 15}, {23, 5, 11}, {23, 11, 7}, {23, 7, 3},
    {23, 3, 20}, {23, 20, 5}, {22, 12, 6}, {22, 6, 21}, {22, 21, 4}, {22, 4, 8}, {22, 8, 12}}]]]

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Johnson Polyhedra

Geometry

Index

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