A cube 30-compound can be constructed from the vertices of the first dodecahedron 6-compound.

It is implemented in the Wolfram Language as `PolyhedronData`[`"CubeThirtyCompound"`,
1].

The cube 30-compound is illustrated above together with its octahedron 30-compound dual and common midsphere.

The common solid and convex hull are unnamed polyhedra illustrated above.