title: Compound of twenty triangular prisms
text: # Compound of twenty triangular prisms
  
  Compound of twenty triangular prisms :
  
  | Type | Uniform compound |
  | - | - |
  | Index | $UC_{33}$ |
  | Polyhedra | 20 triangular prisms |
  | Faces | 40 triangles, 60 squares |
  | Edges | 180 |
  | Vertices | 60 |
  | Symmetry group | icosahedral $(I_h)$ |
  | Subgroup restricting to one constituent | 3-fold dihedral $(D_3)$ |
  
  This uniform polyhedron compound is a symmetric arrangement of 20 triangular prisms, aligned in pairs with the axes of three-fold rotational symmetry of an icosahedron.
  
  It results from composing the two enantiomorphs of the compound of 10 triangular prisms. In doing so, the vertices of the two enantiomorphs coincide, with the result that the full compound has two triangular prisms incident on each of its vertices.
  
  ## Related polyhedra
  
  This compound shares its vertex arrangement with three uniform polyhedra as follows:
  
  | convex hull | Rhombidodecadodecahedron | Icosidodecadodecahedron |
  | - | - | - |
  | Rhombicosahedron | Compound of ten triangular prisms | Compound of twenty triangular prisms |
  