Compound of five octahemioctahedra
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| Compound of five octahemioctahedra | |
|---|---|
| File:UC61-5 octahemioctahedra.png | |
| Type | Uniform compound |
| Index | UC61 |
| Polyhedra | 5 octahemioctahedra |
| Faces | 40 triangles, 20 hexagons |
| Edges | 120 |
| Vertices | 60 |
| 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]
| File:UC61-5 octahemioctahedra.png Traditional filling |
File:5 octahemioctahedra neo filling.png "Neo filling" |
References
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