Thanks for reading my post and responding, dabeard. I thought that there may be some basis for categorizing and subsequently naming zonohedra along these lines. At least group them.
I found out about the relationship between the Zonohedra and the Triangle, in a circuitous way.
I was introduced to a ...

Just to chime in and it may not be of any help, but I would like to point out that Pascal's Triangle can be useful in predicting Zonohedra.

The third row of the triangle, 1,3,3,1.

A regular hexahedron or cube is a zonohedron, there are three unique directions and it makes 3 sets of parallel rhombi ...