A number of attractive 7-compounds of the regular dodecahedron can be constructed.
The compound illustrated above is implemented in the Wolfram Language as PolyhedronData["DodecahedronSevenCompound", 1].
This dodecahedron 7-compound is illustrated above together with its icosahedron 7-compound dual and common midsphere.
The common solid and convex hull are illustrated above.