title: Compound of six pentagonal prisms
text: # Compound of six pentagonal prisms
  
  Compound of six pentagonal prisms :
  
  | Type | Uniform compound |
  | - | - |
  | Index | $UC_{34}$ |
  | Polyhedra | 6 pentagonal prisms |
  | Faces | 12 pentagons, 30 squares |
  | Edges | 90 |
  | Vertices | 60 |
  | Symmetry group | chiral icosahedral (I) |
  | Subgroup restricting to one constituent | 5-fold dihedral $(D_5)$ |
  
  This uniform polyhedron compound is a chiral symmetric arrangement of six pentagonal prisms, aligned with the axes of fivefold rotational symmetry of a dodecahedron.
  
  ## Related polyhedra
  
  This compound shares its vertex arrangement with four uniform polyhedra as follows:
  
  | Nonconvex great rhombicosidodecahedron | Great dodecicosidodecahedron | Great rhombidodecahedron |
  | - | - | - |
  | Truncated great dodecahedron | Compound of six pentagonal prisms | Compound of twelve pentagonal prisms |
  