title: Compound of five cubohemioctahedra
text: # Compound of five cubohemioctahedra
  
  Compound of five cubohemioctahedra :
  
  | Type | Uniform compound |
  | - | - |
  | Index | $UC_{60}$ |
  | Polyhedra | 5 cubohemioctahedra |
  | Faces | 30 squares, 20 hexagons |
  | Edges | 120 |
  | Vertices | 60 |
  | Symmetry group | icosahedral $(I_h)$ |
  | Subgroup restricting to one constituent | pyritohedral $(T_h)$ |
  
  This uniform polyhedron compound is a composition of 5 cubohemioctahedra, in the same arrangement as in the compound of 5 cuboctahedra.
  
  ## Filling
  
  There is some controversy on how to colour the faces of this polyhedron compound. Although the common way to fill in a polygon is to just colour its whole interior, this can result in some filled regions hanging as membranes over empty space. Hence, the "neo filling" is sometimes used instead as a more accurate filling. In the neo filling, orientable polyhedra are filled traditionally, but non-orientable polyhedra have their faces filled with the modulo-2 method (only odd-density regions are filled in). In addition, overlapping regions of coplanar faces can cancel each other out.
  
  | Traditional filling | "Neo filling" |
  | - | - |
  