A Polyhedron Featuring Sixty Heptagons, a Dozen Decagons, Thirty Octagons, and 120 Rectangles, Split Between Two Types at Sixty Each

I made this using Stella 4d: Polyhedron Navigator. This program is available as a free trial download at http://www.software3d.com/Stella.php.

The Dual of a Geodesic Rhombicosidodecahedron

This polyhedron has, as faces, a dozen regular pentagons, thirty rhombi, and sixty irregular heptagons. I made this using Stella 4d, which is available as a free trial download at http://www.software3d.com/Stella.php.