title: Compound of six pentagrammic prisms
text: # Compound of six pentagrammic prisms
  
  Compound of six pentagrammic prisms :
  
  | Type | Uniform compound |
  | - | - |
  | Index | $UC_{36}$ |
  | Polyhedra | 6 pentagrammic prisms |
  | Faces | 12 pentagrams, 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 6 pentagrammic 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:
  
  | Rhombicosidodecahedron | Small dodecicosidodecahedron | Small rhombidodecahedron |
  | - | - | - |
  | Small stellated truncated dodecahedron | Compound of six pentagrammic prisms | Compound of twelve pentagrammic prisms |
  