Compound of five cubohemioctahedra

Compound of five cubohemioctahedra
TypeUniform compound
IndexUC60
Polyhedra5 cubohemioctahedra
Faces30 squares, 20 hexagons
Edges120
Vertices60
Symmetry groupicosahedral (Ih)
Subgroup restricting to one constituentpyritohedral (Th)

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.[1]


Traditional filling

"Neo filling"

References


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