| Compound of five octahedra | |
|---|---|
 (see here for a 3D model) | |
| Type | Regular compound |
| Index | UC17, W23 |
| Coxeter symbol | [5{3,4}]2{3,5}[1] |
| Elements (As a compound) |
5 octahedra: F = 40, E = 60, V = 30 |
| Dual compound | Compound of five cubes |
| Symmetry group | icosahedral (Ih) |
| Subgroup restricting to one constituent | pyritohedral (Th) |
The compound of five octahedra is one of the five regular polyhedron compounds, and can also be seen as a stellation. It was first described by Edmund Hess in 1876. It is unique among the regular compounds for not having a regular convex hull.
- ^ Regular polytopes, pp.49-50, p.98