CunningGabe
commented
1 year ago After talking about this, my opinion has shifted some. I'd almost be inclined to just retire the term "degenerate" since it means different things to different people. (For example, in earlier papers by Egon it means "having a poset that is not a lattice".) On the other hand, the use of "degenerate" to mean "has a 2 in the Schlafli symbol" is fairly standard at this point. So I think I'm inclined to just keep this standard usage, and if I decide I want a term that encompasses more maniplexes / pre-maniplexes than these, then I'll come up with some new term that is more descriptive and less pejorative than "degenerate".
At the moment, IsDegenerate for 3-maniplexes means "has a digonal face or a 2-valent vertex". This is the traditional usage for polyhedra. I'd like to propose an addition: that having a petrie polygon of length 2 should also qualify you as degenerate. For polyhedra with no digons or 2-valent vertices this doesn't occur (I think), which is why it is not part of the usage generally. But I think it would be useful and reasonable to define things this way. Thoughts?