There are a number of attractive polyhedron compounds consisting of six octahedra. The two illustrated above can be constructed as the
duals of cube 6-compounds.
These compounds are implemented in the Wolfram Language as PolyhedronData["OctahedronSixCompound",
These octahedron 6-compounds are illustrated above together with their cube
6-compound duals and common midspheres.
The common solids and convex hulls of these compounds are illustrated above. The interior of the second compound has the connectivity of
the disdyakis dodecahedron.
See alsoCube 6-Compound
, Regular Octahedron
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Cite this as:
Weisstein, Eric W. "Octahedron 6-Compound."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Octahedron6-Compound.html