State-of-the-art article on "uniform 5-polytopes?"

Question

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.”]

Answer 1

There is some information in M.Winter's MSE question, How many uniform polytopes are there in higher dimensions?. There I quote Egon Shulte's "Semiregular and Uniform Convex Polytopes," emphasizing Wythoff's construction.

So possibly this Coxeter paper will help (I am not familiar with it):

Coxeter, H. S. M. "Wythoff's construction for uniform polytopes." Proceedings of the London Mathematical Society 2, no. 1 (1935): 327-339. DOI.