Compound of five octahedra
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| Compound of five octahedra | |
|---|---|
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| Type | Regular compound |
| Stellation core | icosahedron |
| Convex hull | Icosidodecahedron |
| Index | UC17, W23 |
| Polyhedra | 5 octahedra |
| Faces | 40 triangles |
| Edges | 60 |
| Vertices | 30 |
| Dual | Compound of five cubes |
| Symmetry group | icosahedral (Ih) |
| Subgroup restricting to one constituent | pyritohedral (Th) |
This polyhedron can be seen as either a polyhedral stellation or a compound. This compound was first described by Edmund Hess in 1876.
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[edit] As a stellation
It is the second stellation of the icosahedron, and given as Wenninger model index 23.
It can be constructed by a rhombic triacontahedron with rhombic-based pyramids added to all the faces, as shown by the five colored model image.
The stellation facets for construction are:
[edit] As a compound
It can also be seen as a polyhedral compound of five octahedra arranged in icosahedral symmetry (Ih).
It shares the same vertex arrangement as the icosidodecahedron.
[edit] References
- Wenninger, Magnus (1974). Polyhedron Models. Cambridge University Press. ISBN 0-521-09859-9.
- Peter R. Cromwell, Polyhedra, Cambridge, 1997.
- E. Hess 1876 Zugleich Gleicheckigen und Gleichflächigen Polyeder, Schriften der Gesellschaft zur Berörderung der Gasammten Naturwissenschaften zu Marburg 11 (1876) pp 5-97.
