I call the polyhedron above the cubic rhombicosidodecahedroid because it combines a cube’s six squares (shown in green) with the overall appearance of a rhombicosidodecahedron. For comparison, the latter two polyhedra are shown below.

I made these rotating images using Stella 4d: Polyhedron Navigator. This program may be tried for free at http://www.software3d.com/Stella.php.