Compound of five great rhombihexahedra

This uniform polyhedron compound is a composition of 5 great rhombihexahedra, in the same vertex arrangement as the compound of 5 truncated cubes.

Compound of five great rhombihexahedra
TypeUniform compound
IndexUC66
Polyhedra5 great rhombihexahedra
Faces60 squares, 30 octagrams
Edges240
Vertices120
Symmetry groupicosahedral (Ih)
Subgroup restricting to one constituentpyritohedral (Th)

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]


Traditional filling

"Neo filling"

References

  • Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society, 79 (3): 447–457, Bibcode:1976MPCPS..79..447S, doi:10.1017/S0305004100052440, MR 0397554, S2CID 123279687.


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