There are a number of attractive cube 25-compounds. One can be constructed from the vertices of the second dodecahedron 6-compound (or second tetrahedron 50-compound) and another from the vertices of the first tetrahedron 50-compound.

The compounds illustrated above are implemented in the Wolfram Language as `PolyhedronData`[`"CubeTwentyFiveCompound"`,
*n*] for ,
..., 4.

The vertices of the first cube 25-compound lead to attractive an attractive dodecahedron 6-compound, cube 6-compound, and tetrahedron 50-compound, while the second lead to a cube 25-compound and tetrahedron 50-compound (E. Weisstein, Aug. 30, 2023).

The cube 25-compounds are illustrated above together with thier octahedron 25-compound duals and common midspheres.

The common solids and convex hulls are unnamed polyhedra illustrated above.