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.