The image above is a compound of the rhombic triacontahedron (the dual of the icosidodecahedron) and a strombic hexacontahedron (the dual of the rhombicosidodecahedron). Below, you’ll find a compound of six square-based pyramids, all with their “centers of mass” (assuming uniform density) displaced, from the compound’s center, by equal amounts. In response to a request I have received, polyhedral images which rotate more slowly are coming soon . . . after I have finished posting my backlog of already-produced polyhedral .gif files, since there is no way to slow them down after they are already created.
The program I use for these polyhedral investigations is Stella 4d, available at www.software3d.com/Stella.php.