Zonohedra are polyhedra made completely of faces which are zonogons. A zonogon is a polygon which:
- Has an even number of sides,
- Has opposite sides congruent, and
- Has opposite sides parallel.
Parallelograms are the simplest zonogons.
Here is the dual of the zonohedron above; it has 3542 faces. Although zonohedra-duals do have distinctive appearances, they do not, as a class, have a name of their own, to the best of my knowledge. They are definitely not zonohedra, themselves.
Both of these polyhedra were created with Stella 4d, software you may try for yourself, right here.