In[37]:=

Out[37]=

In[38]:=

Out[38]=

In[39]:=

Out[39]=

In[40]:=

Out[40]=

In[41]:=

Out[41]=

In[42]:=

Out[42]=

In[43]:=

Out[43]=

In[44]:=

Out[44]=

In[45]:=

Out[45]//InputForm=

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

In[46]:=

Out[46]=

In[47]:=

Out[47]=

In[48]:=

Out[48]=

Platonic Polyhedra

Dodecahedron 2-Compound
Dodecahedron 5-Compound
Dodecahedron 6-Compound
Dodecahedron-Icosahedron Compound