Compound of five cubohemioctahedra

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Compound of five cubohemioctahedra
UC60-5 cubohemioctahedra.png
Type Uniform compound
Index UC60
Polyhedra 5 cubohemioctahedra
Faces 30 squares, 20 hexagons
Edges 120
Vertices 60
Symmetry group icosahedral (Ih)
Subgroup restricting to one constituent pyritohedral (Th)

This uniform polyhedron compound is a composition of 5 cubohemioctahedra, in the same arrangement as in the compound of 5 cuboctahedra.

Filling[edit]

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]

UC60-5 cubohemioctahedra.png
Traditional filling
5 cubohemioctahedra neo filling.png
"Neo filling"

References[edit]

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