Talk:Uniform polytope

message: I created this stub as I started some articles on higher dimensional uniform polytopes. It's crude, and I appreciate any help to improve it. Thanks!
Tom Ruen 04:41, 6 September 2006 (UTC)
thread_title: Untitled

message: I added a  tag and merged some single-sentence paragraphs in the WP:LEAD.  This article needs help from WP:MSM, specifically, it is seriously in need of .  For example, there is a section, with eight sub-sections and dozens of diagrams, with only a single sentence of prose.  That's unencyclopedic. Orange Knight of Passion (talk) 00:05, 14 September 2008 (UTC)
thread_title:  Confusing 

message: : Special cases of products become hypercubes: ...
True, but the notation shown is for the symmetry groups, not for the polytopes themselves; this is wrong — the symmetry group [4,3] is bigger than the product []×[]×[]. —Tamfang (talk) 19:09, 12 June 2010 (UTC)
replies: text: Rewrite if you like. By symmetry they are all listable, but by geometry (of uniform solutions) and topological result, they're identical, so the question is how far you want to expand the lists. Tom Ruen (talk) 03:08, 13 June 2010 (UTC)
thread_title:  Special case prismatic reductions 

message: : Vertex figures for single-ringed Coxeter-Dynkin diagrams can be constructed from the diagram by removing the ringed node, and ringing neighboring nodes. Such vertex figures are also uniform polytopes, being prismatic if the ringed node was in contact with more than one node.
I'm going to remove the latter sentence.  Such figures are vertex-transitive, but not uniform (faces are not regular) if the arcs from the ringed node are not alike; and they're not prismatic if the parent CD is multiply connected. —Tamfang (talk) 16:27, 6 May 2011 (UTC)
thread_title:  single-ring v.f. 

message: I'm still working on organization for the higher dimensional uniform polytopes, but here's a summary of finite and convex uniform polytope articles. Tom Ruen (talk) 22:43, 3 June 2011 (UTC)
thread_title:  Summary table 

message: "A uniform polytope is a vertex-transitive polytope made from uniform facets of a lower dimension. The uniform polytopes in two dimensions are the regular polygons."
If the definition is the first sentence only, a requirement that all the edges must congruent should be added for consistency within the article. I'm not aware if there's a competing definition of uniformity that permits faces with an even number of edges to have two different alternating lengths, but if there is it's not the most commonly accepted one. If the second sentence is part of the definition, this should be rephrased to make that more clear. 173.227.48.5 (talk) 23:40, 11 April 2013 (UTC)
replies: text: Yes, wording could be improved. Its a recursive definition with defining uniform polygons as regular polygons as the smallest nontrivial dimension, so congruent edges are implied from 2 and up. Tom Ruen (talk) 02:57, 12 April 2013 (UTC)
replies: text: This might be excessively pedantic, but the article appears to consider the line segment to be a uniform polytope. A single vertex and the null polytope might be considered (uniform) polytopes as well. The revised definition only refers to dimensions 2 and up. 173.227.48.5 (talk) 17:07, 12 April 2013 (UTC)
replies: text:  Actually a apeirogon can be considered uniform (rather than regular) if it has alternating 2 colors (types) of edges, which is also a simple truncation t{∞}=t0,1{∞}=. Tom Ruen (talk) 03:55, 26 September 2013 (UTC)
thread_title:  Definition/Lede 

message: The "scaliform" term is really only used by Bowers – unless it is adapted by someone more notable, I don't believe it belongs on this article. I deleted the corresponding section with this justification. Hope it isn't an issue. – OfficialURL (talk) 21:53, 6 April 2020 (UTC)
thread_title:  "Scaliform"