title: Compound of twelve pentagonal prisms
text: # Compound of twelve pentagonal prisms
  
  Compound of twelve pentagonal prisms :
  
  | Type | Uniform compound |
  | - | - |
  | Index | $UC_{35}$ |
  | Polyhedra | 12 pentagonal prisms |
  | Faces | 24 pentagons, 60 squares |
  | Edges | 180 |
  | Vertices | 60 |
  | Symmetry group | icosahedral $(I_h)$ |
  | Subgroup restricting to one constituent | 5-fold dihedral $(D_5)$ |
  
  This uniform polyhedron compound is a symmetric arrangement of 12 pentagonal prisms, aligned in pairs with the axes of fivefold rotational symmetry of a dodecahedron.
  
  It results from composing the two enantiomorphs of the compound of six pentagonal prisms. In doing so, the vertices of the two enantiomorphs coincide, with the result that the full compound has two pentagonal prisms incident on each of its vertices.
  
  ## 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 |
  