A number of attractive 11-compounds of the regular dodecahedron can be constructed.
The compound illustrated above is implemented in the Wolfram Language as PolyhedronData["DodecahedronElevenCompound", 1].
This dodecahedron 11-compound is illustrated above together with its icosahedron 11-compound dual and common midsphere.
The common solid and convex hull are illustrated above.