If you stellate the tetrakis hexahedron once, you get a compound of two pyritohedral dodecahedra.

The 16th stellation is a compound of three elongated octahedra.

Later, when you get to the 65th stellation, the result is a compound of four triangular dipyramids.

I found these compounds, and created these rotating images, using Stella 4d: Polyhedron Navigator. If you wish, you can try this program for free at http://www.software3d.com/Stella.php.