There are a number of attractive polyhedron compounds consisting of seven octahedra. The compound illustrated above can be constructed as the dual of cube 7-compound.
The compound are implemented in the Wolfram Language as PolyhedronData[
"OctahedronSevenCompound",
1
].
These octahedron 7-compounds are illustrated above together with their cube 7-compound duals and common midspheres.
The common solids and convex hulls of these compounds are illustrated above.
