Compound of five octahedra
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. It can also be called a small icosicosahedron.
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.
It has a density of greater than 1.
| Stellation diagram | Stellation core | Convex hull |
Icosahedron | Icosidodecahedron |
As a compound
It can also be seen as a polyhedral compound of five octahedra arranged in icosahedral symmetry.The spherical and stereographic projections of this compound look the same as those of the disdyakis triacontahedron.
But the convex solid's vertices on 3- and 5-fold symmetry axes correspond only to edge crossings in the compound.
Replacing the octahedra by tetrahemihexahedra leads to the compound of five tetrahemihexahedra.