quickfur wrote:Keiji wrote:I know. I refer to ox+o (where x+ = one or more 'x', as in regexp) as rectate for any dimension because of that property, and you can see my names for them in the "conventional" column here. That said, I'm not particularly convinced that my scheme gives good names for the others, but this is because I can't properly visualize most of the non-parent polytopes (yet) so I have no way of knowing what the most natural scheme would be.
Well, all the uniform polytopes arise from the possible combinations of circled and non-circled nodes in the Coxeter-Dynkin diagram for the parent polytope. So that gives us a way of checking whether our naming schemes cover all the possibilities. As for visualizing them... it's really not that hard in the case of 4D; take a look at http://en.wikipedia.org/wiki/Uniform_polychoron - many of the uniform polytopes, especially the pentatopic/tesseractic ones, have nice projection images on their respective pages.
Yes, I've looked all over Wikipedia's uniform polychora pages and images and I still haven't been able to find a scheme which includes all possibilities, has rectates be self-dual and makes sense to the look of the objects. I don't understand, or agree with (due to rectates, if nothing else) the one that's officially accepted and I'm certain there are problems with the one I made up about, what, two and a half years ago. So I've been avoiding really doing much with them since.
I've made a table of the regular polytopes on the wiki now - next is to either rename the appropriate shape pages, or redirect the redlinks to them.