- Compound of five octahedra
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Compound of five octahedra 
Type Regular compound Index UC17, W23 Elements
(As a compound)5 octahedra:
F = 40, E = 60, V = 30Dual compound Compound of five cubes Symmetry group icosahedral (Ih) Subgroup restricting to one constituent pyritohedral (Th) Stellation diagram Stellation core Convex hull 
Icosahedron
IcosidodecahedronThis polyhedron can be seen as either a polyhedral stellation or a compound. This compound was first described by Edmund Hess in 1876.
Contents
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.
As a compound
It can also be seen as a polyhedral compound of five octahedra arranged in icosahedral symmetry (Ih).
It shares its edges and half of its triangular faces with the compound of five tetrahemihexahedra.
Compound of five octahedra
Compound of five tetrahemihexahedraAs a facetting
It is a facetting of the icosidodecahedron, as shown below:
At left only one octahedron is shown; all five are shown at right.
References
- Peter R. Cromwell, Polyhedra, Cambridge, 1997.
- Wenninger, Magnus (1974). Polyhedron Models. Cambridge University Press. ISBN 0-521-09859-9.
- Coxeter, Harold Scott MacDonald; Du Val, P.; Flather, H. T.; Petrie, J. F. (1999). The fifty-nine icosahedra (3rd ed.). Tarquin. ISBN 978-1-899618-32-3. MR676126 (1st Edn University of Toronto (1938))
- E. Hess 1876 Zugleich Gleicheckigen und Gleichflächigen Polyeder, Schriften der Gesellschaft zur Berörderung der Gasammten Naturwissenschaften zu Marburg 11 (1876) pp 5–97.
External links
Notable stellations of the icosahedron Regular Uniform duals Regular compounds Regular star Others Icosahedron Small triambic icosahedron Great triambic icosahedron Compound of five octahedra Compound of five tetrahedra Compound of ten tetrahedra Great icosahedron Excavated dodecahedron Final stellation 
The stellation process on the icosahedron creates a number of related polyhedra and compounds with icosahedral symmetry. 
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