A number of attractive 6-compounds of the regular dodecahedron can be constructed. The first (left figures) can be obtained by combining six dodecahedra, each rotated by 1/10 of a turn about the line joining the centroids of opposite faces (Hart).
A second attractive dodecahedron compound (middle figures) can be constructed from the first cube 20-compound (E. Weisstein, Aug. 30, 2023). This compound is similar in appearance to the dodecahedron 5-compound in that it has pentagonal "dimples," but its "bumps" are more complicated in shape. The vertices of this compound lead to a cube 25-compound and a tetrahedron 50-compound.
These compounds are implemented in the Wolfram Language as PolyhedronData[
"DodecahedronSixCompound",
n
]
for 
and 2.
These dodecahedron 6-compounds are illustrated above together with their icosahedron 6-compound duals and common midspheres.
The common solids and convex hulls are illustrated above.
