The first solid below is the sixth stellation of the triakis octahedron, one of the Catalan solids. It’s also a compound of three square trapezohedra.

The next solid is the 8th stellation of the triakis octahedron, and it’s also a four-part compound of partial cubes.

Finally, here’s the 18th stellation of the triakis octahedron, which is also a compound of six square-based pyramids.