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",
n
]
for 
,
2.
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.
