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|Bowers style acronym||Rhom|
|Vertex figure||Golden hexagram, edge length √2|
|Measures (edge length 1)|
|Convex core||Rhombic triacontahedron|
|Abstract & topological properties|
|Symmetry||H3, order 120|
The rhombihedron, rhom, or compound of five cubes is a uniform polyhedron compound. It consists of 30 squares. The vertices coincide in pairs, leading to 20 vertices where 6 squares join.
It has the same edges as the small ditrigonary icosidodecahedron.
This compound is sometimes considered to be regular, but it is not flag-transitive, despite the fact it is vertex, edge, and face-transitive. It is however regular if you consider conjugacies along with its other symmetries.
Its quotient prismatic equivalent is the cubic pentachoroorthowedge, which is seven-dimensional.
The vertices of a rhombihedron of edge length 1 are given by:
along with all even permutations of:
- Bowers, Jonathan. "Polyhedron Category C1: Compound Regulars" (#4).
- Klitzing, Richard. "rhom".
- Wikipedia Contributors. "Compound of five cubes".