Well, coining "Hart property" was lazy of me. I'll try to come up with something different if I need a name for this property, like "the property in question". On Friday, October 20, 2017, James Propp <jamespropp@gmail.com> wrote:
Okay, I'll write "Hart property" instead of "combinatorially constant width property" until someone suggests a better term. :-)
It seems to me that (if I understood what George wrote in his earlier message) the hexagonal prism, although it is a zonohedron, does NOT have the Hart property, since 6 - 2 n.(a+b+c)/n.(a+b+c+d) depends on n. What am I missing?
What I was missing was something clearly stated in George's email, which I didn't process at the time: the two hexagonal faces can be seen as having three internal edges apiece, and if those are included then the prism *does* have the property in question. This is tantamount to viewing some of the cross-sectional polygons as having adjacent sides that are parallel, i.e. as having extra vertices. Jim Propp