Talk:Uniform 5-polytope

hyperbolic
Seems to me there ought to be (at least) one more hyperbolic family: [4,31,1,1]. —Tamfang (talk) 02:31, 27 July 2010 (UTC)


 * By [James E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge studies in advanced mathematics, 29 (1990), p142] |google book, there are 9 noncompact (nonfinite facets or verf?) hyperbolic Coxeter Groups, including [4,31,1,1]. Tom Ruen (talk) 03:30, 27 July 2010 (UTC)


 * Having looked at my notes (which are in the TV room), I was about to say that, except for the citation part. ;) Glad to know I found 'em all. —Tamfang (talk) 03:33, 27 July 2010 (UTC)


 * Hurray! Very glad for your eagle eyes! Tom Ruen (talk) 03:59, 27 July 2010 (UTC)

little booboo
The CD for honeycomb #136 is (in effect) the same as for #135. —Tamfang (talk) 17:37, 27 July 2010 (UTC)


 * Got it. Tom Ruen (talk) 21:00, 27 July 2010 (UTC)

Element counts
The element counts (number of vertices, edges, 2-faces, 3-faces, and 4-faces) in the tables for the A5 and B5 polytopes seem to be shuffled around. Polymake (the software), with the given coordinates, gives the same counts, but for different polytopes. There are three possible explanations: The given coordinates aren't matched up correctly; the given element counts aren't matched up correctly; or polymake is in error.

In the A5 case, for all but the Runcitruncated 5-simplex, the element counts on the individual pages for each polytope agree with polymake, and that case seems to be an error on the page (as I explained in its own Talk page.) So I went ahead and reordered that table.

In the B5 case, the element counts seem to be universally swapped between forms based on the 5-cube and forms based on the 5-orthoplex; e.g., the element counts listed for the Cantellated 5-orthoplex are those computed for the Cantellated 5-cube, and vice versa. However, in this case the element counts on the individual polytope pages agree with those in the table, for the most part (the only exceptions are the Truncated 5-orthoplex/5-cube and Rectified 5-orthoplex/5-cube, which have element counts on their pages agreeing with polymake, being swapped from the table on this page. Also, the element counts on the pages for the Bitruncated 5-cube and the Runcinated 5-orthoplex agree with polymake, but the corresponding Bitruncated 5-orthoplex and Runcinated 5-cube do not, so they in fact repeat the same element counts twice.)

I think all the counts should be swapped between the 5-orthoplex-based forms and the 5-cube-based forms, but it's also possible that the given coordinates have been swapped. Can someone with a reliable source determine which? --kundor (talk) 17:30, 25 July 2013 (UTC)


 * I also commented at Talk:Runcinated 5-simplex. It looks like your Polymake is correct. If you want verification the Klitzing pages are reliable source, linked under the Bowers Acronyms and Coxeter diagrams. Number may have been accidentally shifted around in building these tables, and clearly specifically there were some low-to-high count reversal errors at least from typing them in. Tom Ruen (talk) 20:26, 25 July 2013 (UTC)


 * OK, I went ahead and changed it, both here and on individual polytope pages. I checked a couple of cases against the Klitzing pages to make sure the vertex-counts, at least, are now correct. (I don't really know how to interpret the rest of the data on those pages.) --kundor (talk) 19:58, 26 July 2013 (UTC)

Reliable sources
A self-posted ms that has not undergone peer review and subsequent publication is not a reliable source and cannot be used as a reference. For more, please see WP:RS. &mdash; Cheers, Steelpillow (Talk) 21:40, 1 February 2015 (UTC)

Original research
It now transpirs that this article contains a good deal of original research. wrotes above; "We can enumerate the permutation of rings in each Coxeter diagram and name them by Johnson, and pretend no one of authority has ever tried counting the elements of each polytope. Actually my Coxeter plane graphs were done by computing the vertex counts as base coordinate permutations and edges counts by minimum distances. I've never tried doing a full "convex hull" search to extract all the element counts and types. At least that's the way I'd verify the numbers if I was worried for error. Even if Norman publishes his book "Uniform polytopes" I have no evidence he's going to give a detailed list of information of all the uniform polytopes of each dimension." This is clearly forbidden by WP:NOR. Is anybody going to contest its removal? &mdash; Cheers, Steelpillow (Talk) 10:52, 2 February 2015 (UTC)
 * Shouldn't it be fine per WP:CALC? Double sharp (talk) 10:48, 3 February 2015 (UTC)
 * Let's have a look at it: "Routine calculations do not count as original research, provided there is consensus among editors that the result of the calculation is obvious, correct, and a meaningful reflection of the sources." Well, there is certainly no consensus with me that it is even one of obvious, correct or does not go beyond the intent of reliable sources, never mind all three. So - no. &mdash; Cheers, Steelpillow (Talk) 11:21, 3 February 2015 (UTC)
 * Fair enough. :-) So I guess if the element counts cannot be sourced yet, then the only thing left is the listing of polytopes. And since these can be constructed by just ringing various nodes of the Coxeter diagram, then I guess the articles for uniform n-polytopes for 5 ≤ n ≤ 10 would be better off merged into a single article just listing the various families and the different operations (truncation, cantellation, etc.), and not listing every single example (we don't know if that is the complete set, after all), Since the convex uniform n-polytopes for n ≤ 4 have been fully enumerated in reliable sources those articles should stay IMO. (By the same token, uniform tiling and convex uniform honeycomb can stay: the rest shouldn't exist as separate articles yet.) Double sharp (talk) 13:29, 4 February 2015 (UTC)
 * I am certainly in favour of collapsing the higher uniform n-polytopes into the uniform polytope article. If any individual polytope is notable (and I believe that some are important in theoretical physics), they deserve their own articles and can be linked individually. There is certainly sufficient evidence to justify the article on the uniform 4-polytopes, but whether the convex ones need their own space is debatable, I need to take a closer look. I also agree about the uniform tilings and convex uniform honeycombs. &mdash; Cheers, Steelpillow (Talk) 15:06, 4 February 2015 (UTC)
 * I think all the basic polytopes (i.e. regulars, demihypercubes, En polytopes) deserve their own articles up to perhaps 10 dimensions (maybe 8 or 9 would work too, though), but I really do not think we need to show the various truncations/rectifications/etc. of these on the same articles. In fact, things like Pentellated 6-simplexes (t0,...,5{35}) probably should not even exist as articles, only as redirects.
 * P.S. I added the qualifier "convex" regarding the uniform 4-polytopes because there's nothing really published on the nonconvex ones besides the regulars (and perhaps the duoprisms like {p/q}×{r/s} and polyhedral prisms like (some uniform polyhedron)×{}). But you have a point: the nonconvex ones should probably be mentioned in the same article, with the caveat that there are many more forms (the 1845 figure can be mentioned and cited to Johnson's abstract, but no more), but they have not been published yet in reliable sources. Double sharp (talk) 15:50, 4 February 2015 (UTC)

P.S. Another problem with the lists for uniform 5-polytopes and above is that they can't be as complete as the lower ones in including nonuniform alternations, simply because those were never published. For example no doubt exists, and is nonuniform due to its omnisnub 5-cell  facets, but you almost certainly won't find that figure in any RS. I guess this is just another manifestation of the fact that much of the material that would make this list benefit from being a standalone article is unsourced and can't be included, and so it is better merged for the time being. Double sharp (talk) 07:10, 7 February 2015 (UTC)

the only uniform star 5-polytopes that can be included
(sidtaxhiap, β2o3o3o5β) and (gadtaxhiap, β2o3o3o5/3β) are the Johnson antiprisms of 5D: if he mentions them in his 1966 thesis (which I think he does) they can be included.

The 4D ones are: or   (sidtidap, β2β5o3o),   (ditdidap, ?), and  or   (gidtidap, β2β5/2o3o). Double sharp (talk) 14:57, 9 February 2015 (UTC)


 * I have no idea on any of these CDs, at least I don't understand holosnubs sufficiently, and don't trust what you're marking. If you can find sources, the 4D Johnson antiprisms named at Norman_Johnson_(mathematician) makes more sense. Tom Ruen (talk) 22:43, 9 February 2015 (UTC)