title: Compound of five great icosahedra
text: # Compound of five great icosahedra
  
  Compound of five great icosahedra :
  
  | Type | Uniform compound |
  | - | - |
  | Index | $UC_{53}$ |
  | Polyhedra | 5 great icosahedra |
  | Faces | 40+60 Triangles |
  | Edges | 150 |
  | Vertices | 60 |
  | Symmetry group | icosahedral $(I_h)$ |
  | Subgroup restricting to one constituent | pyritohedral $(T_h)$ |
  
  This uniform polyhedron compound is a composition of 5 great icosahedra, in the same arrangement as in the compound of 5 icosahedra.
  
  The triangles in this compound decompose into two orbits under action of the symmetry group: 40 of the triangles lie in coplanar pairs in icosahedral planes, while the other 60 lie in unique planes.
  
  