In[204]:=

Out[204]=

In[205]:=

Out[205]=

In[206]:=

Out[206]=

In[207]:=

Out[207]=

In[208]:=

Out[208]=

In[209]:=

Out[209]=

In[210]:=

Out[210]=

In[211]:=

Out[211]//InputForm=

Graphics3D[GraphicsComplex[{{0, 0, Sqrt[9/8 + (3*Sqrt[5])/8]}, {0, 0, -Sqrt[(3*(3 + Sqrt[5]))/2]/2},
   {Sqrt[1/8 - Sqrt[5]/24], (-3 - Sqrt[5])/4, Sqrt[1/8 + Sqrt[5]/24]}, {Sqrt[1/8 - Sqrt[5]/24], (3 + Sqrt[5])/4, Sqrt[1/8 + Sqrt[5]/24]},
   {Sqrt[1/8 + Sqrt[5]/24], -1/2, Sqrt[3/4 + Sqrt[5]/3]}, {Sqrt[1/8 + Sqrt[5]/24], 1/2, Sqrt[3/4 + Sqrt[5]/3]},
   {Sqrt[1/8 + Sqrt[5]/24], (-3 - Sqrt[5])/4, Root[1 - 36*#1^2 + 144*#1^4 & , 2, 0]}, {Sqrt[1/8 + Sqrt[5]/24], (-1 - Sqrt[5])/4,
    -Sqrt[(5*(3 + Sqrt[5]))/6]/2}, {Sqrt[1/8 + Sqrt[5]/24], (1 + Sqrt[5])/4, -Sqrt[(5*(3 + Sqrt[5]))/6]/2},
   {Sqrt[1/8 + Sqrt[5]/24], (3 + Sqrt[5])/4, Root[1 - 36*#1^2 + 144*#1^4 & , 2, 0]}, {Sqrt[5/8 + (5*Sqrt[5])/24], 0, -Sqrt[(3 + Sqrt[5])/6]},
   {Sqrt[5/8 + (5*Sqrt[5])/24], (-1 - Sqrt[5])/4, Sqrt[1/8 + Sqrt[5]/24]}, {Sqrt[5/8 + (5*Sqrt[5])/24], (1 + Sqrt[5])/4, Sqrt[1/8 + Sqrt[5]/24]},
   {-Sqrt[3/4 + Sqrt[5]/3], -1/2, Sqrt[1/8 + Sqrt[5]/24]}, {-Sqrt[3/4 + Sqrt[5]/3], 1/2, Sqrt[1/8 + Sqrt[5]/24]},
   {Sqrt[3/4 + Sqrt[5]/3], -1/2, -Sqrt[(3 + Sqrt[5])/6]/2}, {Sqrt[3/4 + Sqrt[5]/3], 1/2, -Sqrt[(3 + Sqrt[5])/6]/2},
   {Sqrt[9/8 + (3*Sqrt[5])/8], 0, 0}, {-Sqrt[(3 + Sqrt[5])/6], 0, -Sqrt[(5*(3 + Sqrt[5]))/6]/2},
   {-Sqrt[(3 + Sqrt[5])/6]/2, -1/2, -Sqrt[3/4 + Sqrt[5]/3]}, {-Sqrt[(3 + Sqrt[5])/6]/2, 1/2, -Sqrt[3/4 + Sqrt[5]/3]},
   {-Sqrt[(3 + Sqrt[5])/6]/2, (-3 - Sqrt[5])/4, Sqrt[1/8 - Sqrt[5]/24]}, {-Sqrt[(3 + Sqrt[5])/6]/2, (-1 - Sqrt[5])/4,
    Sqrt[5/8 + (5*Sqrt[5])/24]}, {-Sqrt[(3 + Sqrt[5])/6]/2, (1 + Sqrt[5])/4, Sqrt[5/8 + (5*Sqrt[5])/24]},
   {-Sqrt[(3 + Sqrt[5])/6]/2, (3 + Sqrt[5])/4, Sqrt[1/8 - Sqrt[5]/24]}, {Sqrt[(3 + Sqrt[5])/6], 0, Sqrt[5/8 + (5*Sqrt[5])/24]},
   {-Sqrt[(5*(3 + Sqrt[5]))/6]/2, 0, Sqrt[(3 + Sqrt[5])/6]}, {-Sqrt[(5*(3 + Sqrt[5]))/6]/2, (-1 - Sqrt[5])/4, -Sqrt[(3 + Sqrt[5])/6]/2},
   {-Sqrt[(5*(3 + Sqrt[5]))/6]/2, (1 + Sqrt[5])/4, -Sqrt[(3 + Sqrt[5])/6]/2}, {-Sqrt[(3*(3 + Sqrt[5]))/2]/2, 0, 0},
   {Root[1 - 36*#1^2 + 144*#1^4 & , 2, 0], (-3 - Sqrt[5])/4, -Sqrt[(3 + Sqrt[5])/6]/2}, {Root[1 - 36*#1^2 + 144*#1^4 & , 2, 0], (3 + Sqrt[5])/4,
    -Sqrt[(3 + Sqrt[5])/6]/2}}, Polygon[{{24, 15, 14, 23, 1}, {2, 9, 17, 16, 8}, {8, 16, 12, 3, 31}, {16, 17, 13, 26, 12}, {17, 9, 32, 4, 13},
    {9, 2, 19, 29, 32}, {2, 8, 31, 28, 19}, {4, 32, 29, 15, 24}, {29, 19, 28, 14, 15}, {28, 31, 3, 23, 14}, {3, 12, 26, 1, 23},
    {26, 13, 4, 24, 1}, {29, 21, 20, 28, 30}, {18, 13, 6, 5, 12}, {12, 5, 23, 22, 7}, {5, 6, 24, 27, 23}, {6, 13, 10, 25, 24},
    {13, 18, 11, 9, 10}, {18, 12, 7, 8, 11}, {25, 10, 9, 21, 29}, {9, 11, 8, 20, 21}, {8, 7, 22, 28, 20}, {22, 23, 27, 30, 28},
    {27, 24, 25, 29, 30}}]]]

In[212]:=

Out[212]=

In[213]:=

Out[213]=

In[214]:=

Out[214]=