title: Compound of ten triangular prisms
text: # Compound of ten triangular prisms
  
  Compound of ten triangular prisms :
  
  | Type | Uniform compound |
  | - | - |
  | Index | $UC_{32}$ |
  | Polyhedra | 10 triangular prisms |
  | Faces | 20 triangles, 30 squares |
  | Edges | 90 |
  | Vertices | 60 |
  | Symmetry group | chiral icosahedral (I) |
  | Subgroup restricting to one constituent | 3-fold dihedral $(D_3)$ |
  
  This uniform polyhedron compound is a chiral symmetric arrangement of 10 triangular prisms, aligned with the axes of three-fold rotational symmetry of an icosahedron.
  
  ## 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 |
  