I made this using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.
Zome is a ball-and-stick modeling system which can be used to make millions of different polyhedra. If you’d like to get some Zome for yourself, just visit http://www.zometool.com.
The only irregular faces in this polyhedron are the quadrilaterals (kites and rectangles). I made it using Stella 4d, which you can try for yourself — for free — at http://www.software3d.com/Stella.php.
This zonohedron is based on the icosidodecahedron / rhombic triacontahedron compound — more specifically, on its edges. Twelve faces are regular decagons, twenty are regular hexagons, sixty are squares, and the only irregular faces are the thirty equilateral octagons. That’s 122 faces in all.
After I’d posted this, a helpful friend on Facebook told me the official name of the first polyhedron shown here — a pentalofted chamfered dodecahedron.
These images were created using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.