title: Compound of five tetrahemihexahedra
text: # Compound of five tetrahemihexahedra
  
  Compound of five tetrahemihexahedra :
  
  | Type | Uniform compound |
  | - | - |
  | Index | $UC_{18}$ |
  | Polyhedra | 5 tetrahemihexahedra |
  | Faces | 20 triangles, 15 squares |
  | Edges | 60 |
  | Vertices | 30 |
  | Symmetry group | chiral icosahedral (I) |
  | Subgroup restricting to one constituent | chiral tetrahedral (T) |
  
  A compound of five tetrahemihexahedra is a uniform polyhedron compound and a symmetric arrangement of five tetrahemihexahedra. It is chiral with icosahedral symmetry (I).
  
  ## Related polyhedra
  
  Its convex hull is an icosidodecahedron. Hence it is a faceting of an icosidodecahedron, shown at left. It shares its edges and triangular faces with the compound of five octahedra.
  
  | Icosidodecahedron | Compound of five octahedra | Compound of five tetrahemihexahedra |
  | - | - | - |
  