title: Compound of five great rhombihexahedra
text: # Compound of five great rhombihexahedra
  
  Compound of five great rhombihexahedra :
  
  | Type | Uniform compound |
  | - | - |
  | Index | $UC_{66}$ |
  | Polyhedra | 5 great rhombihexahedra |
  | Faces | 60 squares, 30 octagrams |
  | Edges | 240 |
  | Vertices | 120 |
  | Symmetry group | icosahedral $(I_h)$ |
  | Subgroup restricting to one constituent | pyritohedral $(T_h)$ |
  
  This uniform polyhedron compound is a composition of 5 great rhombihexahedra, in the same vertex arrangement as the compound of 5 truncated cubes.
  
  ## 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" |
  | - | - |
  