Hellenica World

Great Stellated Dodecahedron

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Graphics3D[GraphicsComplex[{{Root[1 - 10*#1^2 + 5*#1^4 & , 2, 0], 0, Root[1 - 20*#1^2 + 80*#1^4 & , 4, 0]},
   {Root[1 - 10*#1^2 + 5*#1^4 & , 3, 0], 0, Root[1 - 20*#1^2 + 80*#1^4 & , 1, 0]},
   {Root[1 - 5*#1^2 + 5*#1^4 & , 2, 0], 0, Root[1 - 100*#1^2 + 80*#1^4 & , 3, 0]},
   {Root[1 - 5*#1^2 + 5*#1^4 & , 3, 0], 0, Root[1 - 100*#1^2 + 80*#1^4 & , 2, 0]},
   {Root[1 - 100*#1^2 + 80*#1^4 & , 2, 0], (1 - Sqrt[5])/4, Root[1 - 20*#1^2 + 80*#1^4 & , 4, 0]},
   {Root[1 - 100*#1^2 + 80*#1^4 & , 2, 0], (-1 + Sqrt[5])/4, Root[1 - 20*#1^2 + 80*#1^4 & , 4, 0]},
   {Root[1 - 100*#1^2 + 80*#1^4 & , 3, 0], (1 - Sqrt[5])/4, Root[1 - 20*#1^2 + 80*#1^4 & , 1, 0]},
   {Root[1 - 100*#1^2 + 80*#1^4 & , 3, 0], (-1 + Sqrt[5])/4, Root[1 - 20*#1^2 + 80*#1^4 & , 1, 0]},
   {Root[1 - 40*#1^2 + 80*#1^4 & , 2, 0], -1/2, Root[1 - 100*#1^2 + 80*#1^4 & , 3, 0]},
   {Root[1 - 40*#1^2 + 80*#1^4 & , 2, 0], 1/2, Root[1 - 100*#1^2 + 80*#1^4 & , 3, 0]},
   {Root[1 - 40*#1^2 + 80*#1^4 & , 3, 0], -1/2, Root[1 - 100*#1^2 + 80*#1^4 & , 2, 0]},
   {Root[1 - 40*#1^2 + 80*#1^4 & , 3, 0], 1/2, Root[1 - 100*#1^2 + 80*#1^4 & , 2, 0]},
   {Root[1 - 20*#1^2 + 80*#1^4 & , 1, 0], (1 - Sqrt[5])/4, Root[1 - 100*#1^2 + 80*#1^4 & , 2, 0]},
   {Root[1 - 20*#1^2 + 80*#1^4 & , 1, 0], (-1 + Sqrt[5])/4, Root[1 - 100*#1^2 + 80*#1^4 & , 2, 0]},
   {Root[1 - 20*#1^2 + 80*#1^4 & , 2, 0], (3 - Sqrt[5])/4, Root[1 - 20*#1^2 + 80*#1^4 & , 1, 0]},
   {Root[1 - 20*#1^2 + 80*#1^4 & , 2, 0], (-3 + Sqrt[5])/4, Root[1 - 20*#1^2 + 80*#1^4 & , 1, 0]},
   {Root[1 - 20*#1^2 + 80*#1^4 & , 3, 0], (3 - Sqrt[5])/4, Root[1 - 20*#1^2 + 80*#1^4 & , 4, 0]},
   {Root[1 - 20*#1^2 + 80*#1^4 & , 3, 0], (-3 + Sqrt[5])/4, Root[1 - 20*#1^2 + 80*#1^4 & , 4, 0]},
   {Root[1 - 20*#1^2 + 80*#1^4 & , 4, 0], (1 - Sqrt[5])/4, Root[1 - 100*#1^2 + 80*#1^4 & , 3, 0]},
   {Root[1 - 20*#1^2 + 80*#1^4 & , 4, 0], (-1 + Sqrt[5])/4, Root[1 - 100*#1^2 + 80*#1^4 & , 3, 0]}},
  Polygon[{{13, 4, 1, 7, 17}, {18, 8, 1, 4, 14}, {10, 7, 1, 8, 9}, {19, 3, 2, 5, 15}, {16, 6, 2, 3, 20},
    {12, 5, 2, 6, 11}, {9, 20, 3, 19, 10}, {11, 14, 4, 13, 12}, {17, 15, 5, 12, 13}, {14, 11, 6, 16, 18},
    {15, 17, 7, 10, 19}, {20, 9, 8, 18, 16}}]]]

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"GreatStellatedDodecahedron_18.gif"

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"GreatStellatedDodecahedron_20.gif"

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"GreatStellatedDodecahedron_21.gif"

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"GreatStellatedDodecahedron_22.gif"

Kepler-Poinsot Polyhedra