A Rhombicosidodecahedron, with the Square Faces Rendered Invisible

This polyhedron’s square faces are hidden from view, so that you can see both the front and back of the solid as it rotates. I made this using Stella 4d: Polyhedron Navigator, which you can try for yourself, free, at http://www.software3d.com/Stella.php.

Rhombicosidodeca