This polyhedron was created by performing vertex-based zonohedrifications of a dodecahedron — twice. The first zonohedrification produced a rhombic enneacontahedron, various version of which I have blogged many times before, but performing a second zonohedrification of the same type was a new experiment. It has 1230 faces, 1532 vertices, and 2760 edges. All of its edges have equal length. I created the models in this post using Stella 4d, a program you can buy, or try for free, right here.

Here is the dual of this zonohedron, which has 1532 faces, 1230 vertices, and 2760 edges. This “flipping” of the numbers of faces and vertices, with the number of edges staying the same, always happens with dual polyhedra. I do not know of a name for the class of polyhedra made of zonohedron-duals, but, if any reader of this post knows of one, please leave this name in a comment.