Stella 4d, a program you can try here, was used to create these two compounds. Both have pyritohedral symmetry: the symmetry of a standard volleyball. The two compounds are also duals.
That’s the compound of the dodecahedron and the truncated octahedron above. Shown next is its dual, the compound of the icosahedron and the tetrakis cube. Both compounds were made using Stella 4d: Polyhedron Navigator, which you may try here.
The next one is a compound of eight off-center pyramids. By this point, I had gone so far into the stellation-series (a search I began when preparing the post before this one) that I had lost count.
This one is a compound of three short square-based dipyramids:
This one, according to Stella 4d, is a compound of three parts, but I can’t quite figure out what the parts are!
Here is another “mystery compound,” this one with two parts:
Stella 4d, which I used to make these, may be tried here.