I would like to read article(s) that provide the “state of the art” on the following open problem:
“Enumerate all convex uniform 5-polytopes.”
This problem is posted on the “Open Problem Garden” (http://garden.irmacs.sfu.ca/op/convex_uniform_5_polytopes), but no citation is given. (The same open problem is also listed on Wikipedia’s “List of unsolved problems” (https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_mathematics), but Wikipedia only cites the same “Open Problem Garden” page).
Does anyone know of a legitimate source stating that this is an open problem—especially, of any source(s) that also provide the current mathematical knowledge on this topic?
[Note: I have already looked at all four articles listed on Wikipedia’s “Uniform 5-Polytope” page (https://en.wikipedia.org/wiki/Uniform_5-polytope): H.S.M. Coxeter’s “Regular and Semi-Regular Polytopes I, II, and III” and Norman W. Johnson’s dissertation, “The Theory of Uniform Polytopes and Honeycombs.”]