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Compound of five octahedra
From Wikipedia, the free encyclopedia
| Compound of five octahedra | |
|---|---|
 |
|
| Type | Compound and stellation |
| Polyhedra | 5 octahedra |
| Faces | 40 triangles |
| Edges | 60 |
| Vertices | 30 |
| Dual | Compound of five cubes |
| Symmetry group | icosahedral (Ih) |
This polyhedron can be seen as either a polyhedral stellation or a compound. This compound was first described by Edmund Hess in 1876.
Contents |
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.
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:
- 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.
