Compound of five great rhombihexahedra

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Compound of five great rhombihexahedra
UC66-5 great rhombihexahedra.png
Type Uniform compound
IndexUC66
Polyhedra5 great rhombihexahedra
Faces60 squares, 30 octagrams
Edges240
Vertices120
Symmetry group icosahedral (Ih)
Subgroup restricting to one constituent pyritohedral (Th)

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. [1]

UC66-5 great rhombihexahedra.png
Traditional filling
5 great rhombihexahedra neo filling.png
"Neo filling"

References