This is the second tetstell of the icosidodecahedron. Tetstelling is like normal stellation, except you drop the symmetry of the model to tetrahedral first. It’s an easy trick with Stella 4d, the program I used to make this. You can try it, free, at this website.

Here it is, in the colors Stella chose when I made it again, just now, to double-check those “dozens” in the title of this post.