Regolo's Torus

I was looking to generalize this, but that was before I really understood what was going on. Not a lot of choices to be made! On the other hand, that means a lot of structure to uncover. [br][br]Regolo's original: [url]http://regolo54.tumblr.com/post/134846719037/polyhedra[/url][br][br]Why does this structure produce or require parallelograms?

Information: Regolo's Torus