| bgcolor=#e7dcc3 colspan=2 | Compound of five octahedra | |
|---|---|---|
| align=center colspan=2 | (see here for a 3D model) | |
| bgcolor=#e7dcc3 width=50% | Type | Regular compound |
| Index | UC17, W23 | |
| Coxeter symbol | [5{3,4}]2[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) |
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. (This construction does not generate the regular compound of five octahedra, but shares the same topology and can be smoothly deformed into the regular compound.)
It has a density of greater than 1.
It can also be seen as a polyhedral compound of five octahedra arranged in icosahedral symmetry (Ih).
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 (gray in the images below) correspond only to edge crossings in the compound.
Replacing the octahedra by tetrahemihexahedra leads to the compound of five tetrahemihexahedra.
A second 5-octahedra compound, with octahedral symmetry, also exists. It can be generated by adding a fifth octahedra to the standard 4-octahedra compound.
. Magnus Wenninger . Polyhedron Models . Cambridge University Press . 1974 . 0-521-09859-9 .