There are a number of attractive polyhedron compounds consisting of 25 octahedra.
These compounds are implemented in the Wolfram Language as PolyhedronData[
"OctahedronTwentyFiveCompound",
n
]
for 
,
2, 3.
These octahedron 25-compounds are illustrated above together with their cube 25-compound duals and common midspheres.
The common solids and convex hulls of these compounds are illustrated above.
