Compound of five octahemioctahedra

Last updated
Compound of five octahemioctahedra
UC61-5 octahemioctahedra.png
Type Uniform compound
IndexUC61
Polyhedra5 octahemioctahedra
Faces40 triangles, 20 hexagons
Edges120
Vertices60
Symmetry group icosahedral (Ih)
Subgroup restricting to one constituent pyritohedral (Th)

In geometry, this uniform polyhedron compound is a composition of 5 octahemioctahedra, in the same vertex arrangement as in the compound of 5 cuboctahedra. It could also be called an icosidisicosahedron.

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. Usage of the "neo filling" makes the compound of five octahemioctahedra a hollow polyhedron compound. [1]

UC61-5 octahemioctahedra.png
Traditional filling
5 octahemioctahedra neo filling.png
"Neo filling"

References