In[254]:=

Out[254]=

In[255]:=

Out[255]=

In[256]:=

Out[256]=

In[257]:=

Out[257]=

In[258]:=

Out[258]=

In[259]:=

Out[259]=

In[260]:=

Out[260]=

In[261]:=

Out[261]=

In[262]:=

Out[262]//InputForm=

Graphics3D[GraphicsComplex[
  {{0, (-1 - Sqrt[5])/2, -1 + (154425 - 45*Sqrt[5] - Sqrt[2650294450 - 213518390*Sqrt[5]])/
      319840}, {0, (-1 - Sqrt[5])/2, (154425 - 45*Sqrt[5] -
      Sqrt[2650294450 - 213518390*Sqrt[5]])/319840}, {0, (1 + Sqrt[5])/2,
    -1 + (154425 - 45*Sqrt[5] - Sqrt[2650294450 - 213518390*Sqrt[5]])/319840},
   {0, (1 + Sqrt[5])/2, (154425 - 45*Sqrt[5] - Sqrt[2650294450 - 213518390*Sqrt[5]])/319840},
   {Sqrt[1/2 + 1/(2*Sqrt[5])], 0, Sqrt[(5 - Sqrt[5])/10] +
     (154425 - 45*Sqrt[5] - Sqrt[2650294450 - 213518390*Sqrt[5]])/319840},
   {Sqrt[(5 - Sqrt[5])/10]/2, (-1 - Sqrt[5])/4, Sqrt[(5 - Sqrt[5])/10] +
     (154425 - 45*Sqrt[5] - Sqrt[2650294450 - 213518390*Sqrt[5]])/319840},
   {Sqrt[(5 - Sqrt[5])/10]/2, (1 + Sqrt[5])/4, Sqrt[(5 - Sqrt[5])/10] +
     (154425 - 45*Sqrt[5] - Sqrt[2650294450 - 213518390*Sqrt[5]])/319840},
   {-Sqrt[5/8 + Sqrt[5]/8], (-3 - Sqrt[5])/4,
    -1 + (154425 - 45*Sqrt[5] - Sqrt[2650294450 - 213518390*Sqrt[5]])/319840},
   {-Sqrt[5/8 + Sqrt[5]/8], (-3 - Sqrt[5])/4,
    (154425 - 45*Sqrt[5] - Sqrt[2650294450 - 213518390*Sqrt[5]])/319840},
   {-Sqrt[5/8 + Sqrt[5]/8], (3 + Sqrt[5])/4,
    -1 + (154425 - 45*Sqrt[5] - Sqrt[2650294450 - 213518390*Sqrt[5]])/319840},
   {-Sqrt[5/8 + Sqrt[5]/8], (3 + Sqrt[5])/4,
    (154425 - 45*Sqrt[5] - Sqrt[2650294450 - 213518390*Sqrt[5]])/319840},
   {Sqrt[5/8 + Sqrt[5]/8], (-3 - Sqrt[5])/4,
    -1 + (154425 - 45*Sqrt[5] - Sqrt[2650294450 - 213518390*Sqrt[5]])/319840},
   {Sqrt[5/8 + Sqrt[5]/8], (-3 - Sqrt[5])/4,
    (154425 - 45*Sqrt[5] - Sqrt[2650294450 - 213518390*Sqrt[5]])/319840},
   {Sqrt[5/8 + Sqrt[5]/8], (3 + Sqrt[5])/4,
    -1 + (154425 - 45*Sqrt[5] - Sqrt[2650294450 - 213518390*Sqrt[5]])/319840},
   {Sqrt[5/8 + Sqrt[5]/8], (3 + Sqrt[5])/4,
    (154425 - 45*Sqrt[5] - Sqrt[2650294450 - 213518390*Sqrt[5]])/319840},
   {-Sqrt[1/4 + 1/(2*Sqrt[5])], -1/2, Sqrt[(5 - Sqrt[5])/10] +
     (154425 - 45*Sqrt[5] - Sqrt[2650294450 - 213518390*Sqrt[5]])/319840},
   {-Sqrt[1/4 + 1/(2*Sqrt[5])], 1/2, Sqrt[(5 - Sqrt[5])/10] +
     (154425 - 45*Sqrt[5] - Sqrt[2650294450 - 213518390*Sqrt[5]])/319840},
   {-Sqrt[5/4 + Sqrt[5]/2], -1/2,
    -1 + (154425 - 45*Sqrt[5] - Sqrt[2650294450 - 213518390*Sqrt[5]])/319840},
   {-Sqrt[5/4 + Sqrt[5]/2], -1/2, (154425 - 45*Sqrt[5] - Sqrt[2650294450 - 213518390*Sqrt[5]])/
     319840}, {-Sqrt[5/4 + Sqrt[5]/2], 1/2,
    -1 + (154425 - 45*Sqrt[5] - Sqrt[2650294450 - 213518390*Sqrt[5]])/319840},
   {-Sqrt[5/4 + Sqrt[5]/2], 1/2, (154425 - 45*Sqrt[5] - Sqrt[2650294450 - 213518390*Sqrt[5]])/
     319840}, {Sqrt[5/4 + Sqrt[5]/2], -1/2,
    -1 + (154425 - 45*Sqrt[5] - Sqrt[2650294450 - 213518390*Sqrt[5]])/319840},
   {Sqrt[5/4 + Sqrt[5]/2], -1/2, (154425 - 45*Sqrt[5] - Sqrt[2650294450 - 213518390*Sqrt[5]])/
     319840}, {Sqrt[5/4 + Sqrt[5]/2], 1/2,
    -1 + (154425 - 45*Sqrt[5] - Sqrt[2650294450 - 213518390*Sqrt[5]])/319840},
   {Sqrt[5/4 + Sqrt[5]/2], 1/2, (154425 - 45*Sqrt[5] - Sqrt[2650294450 - 213518390*Sqrt[5]])/
     319840}}, Polygon[{{17, 7, 4, 11}, {16, 17, 21, 19}, {6, 16, 9, 2}, {5, 6, 13, 23},
    {7, 5, 25, 15}, {15, 4, 7}, {11, 21, 17}, {19, 9, 16}, {2, 13, 6}, {23, 25, 5},
    {7, 17, 16, 6, 5}, {24, 22, 12, 1, 8, 18, 20, 10, 3, 14}, {14, 3, 4, 15}, {3, 10, 11, 4},
    {10, 20, 21, 11}, {20, 18, 19, 21}, {18, 8, 9, 19}, {8, 1, 2, 9}, {1, 12, 13, 2},
    {12, 22, 23, 13}, {22, 24, 25, 23}, {24, 14, 15, 25}}]]]

In[263]:=

Out[263]=

In[264]:=

Out[264]=

In[265]:=

Out[265]=

Johnson Polyhedra