Compound of five cubes
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| Compound of five cubes | |
|---|---|
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| Type | Regular compound |
| Stellation core | rhombic triacontahedron |
| Convex hull | Dodecahedron |
| Index | UC9 |
| Polyhedra | 5 cubes |
| Faces | 30 squares |
| Edges | 60 |
| Vertices | 20 |
| Dual | Compound of five octahedra |
| Symmetry group | icosahedral (Ih) |
| Subgroup restricting to one constituent | pyritohedral (Th) |
This polyhedral compound is a symmetric arrangement of five cubes. This compound was first described by Edmund Hess in 1876.
It is one of five regular compounds, and dual to the compound of five octahedra.
It is one of the stellations of the rhombic triacontahedron.
It has icosahedral symmetry (Ih), and its convex hull is a dodecahedron. It shares the same vertex arrangement as the regular dodecahedron. It shares the same edge arrangement as the small ditrigonal icosidodecahedron, the great ditrigonal icosidodecahedron, and the ditrigonal dodecadodecahedron.
The compound of ten tetrahedra can be formed by taking each of these five cubes and replacing them with the two tetrahedra of the Stella octangula (which share the same vertex arrangement of a cube).
[edit] As a stellation
This compound can be formed as a stellation of the rhombic triacontahedron. The 30 rhombic faces exist in the planes of the 5 cubes.
The stellation facets for construction are:
