| bgcolor=#e7dcc3 colspan=2 | Compound of five octahemioctahedra | |
|---|---|---|
| align=center colspan=2 | ||
| Type | Uniform compound | |
| Index | UC61 | |
| Polyhedra | 5 octahemioctahedra | |
| Faces | 40 triangles, 20 hexagons | |
| Edges | 120 | |
| Vertices | 60 | |
| Symmetry group | icosahedral (Ih) | |
| Subgroup restricting to one constituent | pyritohedral (Th) |
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. Usage of the "neo filling" makes the compound of five octahemioctahedra a hollow polyhedron compound.[1]