A Polyhedron Formed by Repeatedly Stellating the Triakis Octahedron, Along With Its Dual

I made these virtual models using Stella 4d, which you can try for yourself, for free, at http://www.software3d.com/Stella.php.

A Cube, Held Prisoner by a Stella Octangula

I made this three-part compound using Stella 4d (available here) to repeatedly tetstell a truncated octahedron.