Talk:Uniform 4-polytope

message: The uniform polychora lists are moved here from Polychora. Some things that need to be done:
* Reorganize this page so that regular polychora and semiregular 4-polytopes appear somewhere sensible. Currently only a subset of regular polychora is described, under convex regular 4-polytope.
* At least some general description of non-convex uniform polychora should be here, under its own heading (does anyone knows what are the 29 categories referred to in the 2nd paragraph? I copied that from the polychoron page; I'm not sure who wrote it nor where I can look it up).
* Some explanation for the names of various polychora:
** What does "cantellated" mean, for example?
** Or "runcinated" or "runcitruncated"?
** What precisely is the difference between "truncated" and "bitruncated"?
—Tetracube 07:15, 10 January 2006 (UTC)
replies: text: I've made a stab at defining some of the operations, as well as some other changes suggested by George Olshevsky. —Anton Sherwood 00:27, 13 January 2006 (UTC)
replies: text: Thanks! That helps a lot.—Tetracube 07:08, 13 January 2006 (UTC)
thread_title: Untitled

message: How do you like my first table?  (I must dash now, will make the others later.)  Someone besides me should check it against .  --Anton Sherwood 18:46, 10 January 2006 (UTC)
replies: text: I like it! Although, it seems that you didn't link each polychoron to its own page. I'll add in those links (some of them already exist as separate pages).—Tetracube 18:59, 10 January 2006 (UTC)
thread_title:  table of corresponding elements 

message: I saw polychora articles updated for new name here. I was thinking, do we want a :Category:Polychora or :Category:Polychoron or :Category:Uniform polychora or :Category:Uniform polychoron?
Currently they are under :Category:Polytopes which isn't bad, except for not specifying 4D objects, although not much going on above 4D yet! Tom Ruen 06:30, 7 February 2006 (UTC)
replies: text: I noticed that :Category:Polytopes already has sub-categories for polygons and polyhedra. Maybe we should move the current polychora into :Category:Polychora, at the very least?—Tetracube 08:20, 8 February 2006 (UTC)
thread_title:  New category? 

message: * 
*# Thorold Gosset - halfregular Polytope was compound in n dimensions from different, but for even regular Polytopen lower dimension.
*# Alicia Boole Stott - permitted the Archimedean polyhedrons as parts of the Polytope. 
*# Norman Woodason Johnson 
*# Willem Abraham Wythoff 
*# John Horton Conway and Mike J.T. Guy
*#* Only Conway and Guy worked in the early 1960's on a first proof; however only a bilateral summary was published.
*# Branko Grünbaum
I removed reference to the open research article Uniform Polychora Project and added a draft history section using information above. Unfortunately fuzzy in details, but a start. Tom Ruen 19:32, 15 July 2006 (UTC)
replies: text: Has someone actually held these sources in their hands and verified that the material in this article appears in the book? CMummert 01:16, 16 July 2006 (UTC)

text: Ah, yeah - one disaster at a time! So far, I've only seen the 1954 "Uniform Polyhedra" paper reference which only covers the list of uniform polyhedra, but I'm in process of seeing what I can get access to by a friend at the University. As a last resort I've been in past email contact with Johnson, Grumbaum, and Conway. Tom Ruen 01:22, 16 July 2006 (UTC)

text: The question is not interest.  The subject is, I agree, interesting.  The question is the existence of printed, reliable sources for the information.  That is the criteria that has been established.   CMummert 03:59, 16 July 2006 (UTC)
thread_title:  Who discovered the uniform polychora? And when? 

message: As a first test, I added cell/face/edge/vertex counts to the 5-cell family. I'm also interested in adding columns for face counts by type, and cells per vertex, but don't want the table too wide, so I'll leave out for now. 
Tom Ruen 21:17, 20 July 2006 (UTC)
thread_title:  Expanding data tables 

message: There are now stub articles for all of the first 48 forms. If anyone wants to help fill in data, I've put a summary data table at: User:Tomruen/uniform_polychoron_table. This independent source should agree with George O's data at     , etc, although I've not compared all of them. My spare time is pretty much gone for the rest of August. Thanks! Tom Ruen 04:48, 14 August 2006 (UTC)
thread_title:  Data completion 

message: I wonder if this should be renamed to Convex uniform polychoron, since there is actually zero content on nonconvex forms?
This would parallel names for convex regular polychoron and convex uniform honeycomb. Polychoron could reference the existence of nonconvex forms. 
Tom Ruen 03:02, 18 September 2006 (UTC)
thread_title:  Rename? 

message: See Talk:Cantellated 5-cell if you have interest or opinions on projection terminology. Thanks! Tom Ruen 22:26, 3 January 2007 (UTC)
thread_title:  Polychoron image projections 

message: I added Coxeter-Dynkin diagram for most of the figures, and expanded tables for the prismatic forms. New tables need elements cross-checked for correctness. I'll try to expand some more sample tables at the end for smallest duoprisms. I'm done for the weekend, except maybe a bit of cross-checking...
This article is getting a bit long, but I like them all in one article. Perhaps useful to consider at some point a List of uniform polychora parallel to List of uniform polyhedra. Then this article could have tables reduced to less information perhaps. 
Tom Ruen 14:34, 20 January 2007 (UTC)
thread_title:  Coxeter-Dynkin diagrams 

message: I'm trying out some new images, making some consistent sets between truncated forms within each class. First test run done on simplex family, centering on cell pos. 3, and showing cells at pos. 0. Seems a good start. Tom Ruen 03:01, 16 March 2007 (UTC)
thread_title:  New image notes 

message: [This paragraph is ambiguous in the extreme. I THINK this is what is meant:]
There are three families of uniform polychora that are considered prismatic:
:Polyhedral prisms
:Duoprisms
:Polygonal prismatic prisms
These prisms generalize the properties ...
[Under each of these 3 heading belong the following lead sentences:]
Polyhedral prisms
The first family contains three subsets: Tetrahedral prisms, Octahedral prisms, and Icosahedral prisms. They are the most obvious family of prismatic polychora, i.e. products of a polyhedron ...
Duoprisms: ...
The second family is the infinite set of duoprisms–products of two regular polygons. The snubbed form–prisms of anti-prisms–is excluded.
Their Coxeter-Dynkin diagram ...
Polygonal prismatic prisms: ...
The third family contains two subsets: Prismatic prisms and Anti-prismatic prisms. Both subsets are infinite.
The prismatic prisms overlap with ...
The anti-prismatic prisms are constructed ...
[However, I do not want to make edit changes, if I am wrong. Further, I believe "prisms of anti-prisms" are the same as "Anti-prismatic prisms" and should be cross referenced--i.e. "excluded" replaced by "included in the third family".]
18:52, 29 January 2011 Colin.campbell.27
: I agree that paragraph needs improvement. I'll try my hand. —Tamfang (talk) 21:17, 29 January 2011 (UTC)
thread_title: Prismatic uniform polychora

message: The numbers don't add up.
Where does the "75" come from? Where are they? I can't get to "75 nonprismatic uniform polyhedra" from "64 convex uniform polychora".
Do the two references to "18 convex" refer to the same set of prisms? (I assume they do.)
22 prisms are listed. 5 of them are duplicates (within "[ ]"). 1 of these is the cube-prism/tesseract. Does 18 = 22 – 5 + 1?
Clarification is needed.
18:52, 29 January 2011 Colin.campbell.27
: (Next time use the template .)
: There's no reason to expect the number of nonprismatic uniform polyhedra to relate to the number of convex polychora.
: Yes, the 18 convex polyhedron-prisms are made from 18 convex polyhedra, four of which are listed twice.  (I think this article would not suffer much if the "rectified-tetrahedral prism" and so on were dropped.) —Tamfang (talk) 21:14, 29 January 2011 (UTC)
replies: text: Right. There's no nonconvex polychora listed here. Tom Ruen (talk) 22:39, 29 January 2011 (UTC)
thread_title: Polyhedral prisms

message: I'm still checking, but here's a first pass list of 3-sphere symmetry groups, in Coxeter's notation (From Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591], mostly from a single table). There's definitely more lower symmetry groups unlisted!
When it looks solid, I'll make an article list List_of_spherical_symmetry_groups (for 2-sphere groups), and link to this under the stat tables for the uniform 4-polytopes. Currently it links to Coxeter group which is really only the pure reflectional symmetries of the Coxeter-Dynkin graphs. Tom Ruen (talk) 03:13, 24 May 2011 (UTC)
replies: text: Where you write "3-sphere symmetry groups", do you mean "finite subgroups of O(4)" ???  (Where of course O(4) denotes the full isometry group of the 3-sphere.)  Or something else?50.205.142.50 (talk) 17:20, 26 June 2020 (UTC)

text: Maybe someday I'll grok these notations. ‹sigh› —Tamfang (talk) 06:12, 29 May 2011 (UTC)
replies: text:  Maybe not too bad on a soft view.  is a doubling of the symmetry of symmetric linear groups, so 3,3 ~= [4,3]. + is a half symmetry by rotation [4,3]+ ~= [3,3]. And also [4,3+] is another half symmetry if next to an even number of reflections. Also [3[31,1,1]] makes all 3 branches identical with 6x symmetry order, ~= [3,4,3]! Tom Ruen (talk) 06:37, 29 May 2011 (UTC)
replies: text:  Geometry was easier than this when I was in school :( jni (talk) 18:09, 23 November 2013 (UTC)
thread_title:  Symmetry groups

message: Is the word "alterated" in the article an accepted technical term? I don't find it in dictionaries.
:The correct term is alternated. I fixed one typo alterated, which was missing the n. Tom Ruen (talk) 19:58, 7 August 2014 (UTC)
thread_title:  "alterated" or "altered" 

message: There is a relevant discussion at Talk:4-polytope#Unknown_total_number_of_nonconvex_uniform_4-polytopes — Cheers, Steelpillow (Talk) 11:05, 19 December 2014 (UTC)
thread_title:  Non-convexes and the UPP 

message: We have them for all the nonprismatics, and I'm uploading some prismatic examples. Since these are rather prominent visualization aids for the polychora perhaps we could add them in their own column. Double sharp (talk) 08:14, 8 February 2015 (UTC)
replies: text: OK, uploaded pictures for the nets of all the p,q-duoprisms for 3 ≤ p,q ≤ 10. Double sharp (talk) 08:24, 8 February 2015 (UTC)
replies: text: ...and all the p-antiprismatic prisms for 4 ≤ p ≤ 10. Double sharp (talk) 08:28, 8 February 2015 (UTC)
thread_title:  nets of the uniform polychora? 

message: I re-added a short description on the uniform star polychora. The fact that they're on a program (Stella4D) where they can visualized surely makes the claims about their existence credible? If some other mathematician has mentioned them during the last few years, a source would be helpful. – OfficialURL (talk) 18:26, 21 February 2020 (UTC)
replies: text: Wait, so this has in fact been topic of heated past discussion over at Talk:4-polytope, and the general consensus is that, since no published article exists on them, they don't belong here on Wikipedia. I'll comment out my edit, in case it ever becomes something that can be added. (I really hope the Norman Johnson manuscript comes out soon). – OfficialURL (talk) 00:11, 22 February 2020 (UTC)
replies: text:  It appears that Johnson left the manuscript almost complete on his death and that a publication is forthcoming. (Although it has been forthcoming since 1996...) Double sharp (talk) 17:55, 22 February 2020 (UTC)
replies: text: Jonathan Bowers wrote up a presentation for the Bridges conference in 2000. Unfortunately, it is so old that there were then 8186 uniform polychora, mostly exotic-celled. Double sharp (talk) 20:54, 21 October 2022 (UTC)
thread_title:  Star polychora 

message: Much of this article is written in obfuscatory language than anyone not intimately familiar with the technical terminology of polytopes is certain will be certain to find confusing.
Additionally, many other things are extremely unclear.
This is very unfortunate, because some Wikipedia writers have made great efforts to fill Wikipedia with extremely comprehensive information about polytopes, and 4-dimensional polytopes in particular.
For example, the very first table of this article is filled with information. But nobody knows what this table is for, because it is entirely unlabeled and has no caption.
I hope anyone who might like to improve this article, and who is familiar with the subject matter and who knows how to write clearly for a non-expert audience, will do so.50.205.142.50 (talk) 20:22, 14 June 2020 (UTC)
thread_title:  Serious problems with this article 

message: One sentence reads as follows:
"The 5-cell has diploid pentachoric [3,3,3] symmetry,[7] of order 120, isomorphic to the permutations of five elements, because all pairs of vertices are related in the same way."
But isn't it necessary for — not just all pairs of vertices — but all vertices, as well as pairs, triples, and quadruples of vertices to be each related in the same way ... in order for the symmetry group to consist of all permutations of the vertices?50.205.142.50 (talk) 17:17, 26 June 2020 (UTC)
thread_title:  This does not seem to be enough to explain it. 

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thread_title:  Commons files used on this page or its Wikidata item have been nominated for deletion