Talk:Uniform 5-polytope

hyperbolic

Seems to me there ought to be (at least) one more hyperbolic family: [4,3^1,1,1]. —Tamfang (talk) 02:31, 27 July 2010 (UTC)[reply]

By [James E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge studies in advanced mathematics, 29 (1990), p142] book, there are 9 noncompact (nonfinite facets or verf?) hyperbolic Coxeter Groups, including [4,3^1,1,1]. Tom Ruen (talk) 03:30, 27 July 2010 (UTC)[reply]

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)[reply]

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

little booboo

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

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

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)[reply]

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. [1] 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)[reply]

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)[reply]

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. — Cheers, Steelpillow (Talk) 21:40, 1 February 2015 (UTC)[reply]

External links

According to WP:LINKSTOAVOID, these include:

"2. Any site that misleads the reader by use of factually inaccurate material or unverifiable research, except to a limited extent in articles about the viewpoints that the site is presenting."

...

"11. Blogs, personal web pages and most fansites, except those written by a recognized authority."

I would say that every single one of the sites listed falls foul of those criteria. Several of them present unverifiable research, and none is a recognized authority that I am aware of. Does anybody have a case for keeping any of them? — Cheers, Steelpillow (Talk) 22:00, 1 February 2015 (UTC)[reply]

You know I'm not going to support removing all of them. A "recognized authority" is in the eye of the beholder. If Klitzing's webpages are unacceptable, there's not much that can be done about anything. Coxeter only gives general theory and various examples. 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. Tom Ruen (talk) 00:36, 2 February 2015 (UTC)[reply]

From WP:USERG; "Self-published material may sometimes be acceptable when its author is an established expert whose work in the relevant field has been published by reliable third-party publications." To my knowledge Richard does not meet this criterion. On the face of it your fear that there is not much tha can be done about anything is spot on. You may not want to support removal but you may not be able to stop it either. Do you wish to take the issue to the wider community? — Cheers, Steelpillow (Talk) 10:44, 2 February 2015 (UTC)[reply]

These websites have related materials to this article, and were removed by Steelpillow.

George Olshevsky (2006), Uniform Panoploid Tetracombs, manuscript. Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs.
Klitzing, Richard. "5D uniform polytopes (polytera)".

Its not clear to me how anyone can establish ANY website with original research of any sort as "verified". There is no clear validation process. This website doesn't even have a personal name associated with it http://www.abstract-polytopes.com/atlas . Self-dual polyhedron website here has a name David I. McCooey, http://dmccooey.com/polyhedra/SymmetricSelfDuals.html. George W. Hart has his virtual reality polyhedra website http://www.georgehart.com/virtual-polyhedra/vp.html . Eclipse data here http://www.mreclipse.com/ at least can be traced to Fred Espenak. Journalist Bob King writes an astronomy blog, widely quoted on Wikipedia, and he is responsible for all his potential errors: http://astrobob.areavoices.com . Mathworld is largely maintained by a single person, Eric W. Weisstein, and has a wide number of uncorrected errors.

Who decides which of these are worthy primary or secondary sources? Tom Ruen (talk) 16:38, 2 February 2015 (UTC)[reply]

Have you not read WP:RS, WP:VERIFICATION, WP:CITE and so on? Briefly, a recognized authority will have an established track record of peer-reviewed publications, and those publications will have been cited by other reliable authors. For example, George Hart is a recognized authority on this basis but George Olshevsky and Richard Klitzing are not. As such, much of George's self-published web material passes condition 11. above, while Olshevsky and Klitzing do not. In particular, just because someone distills their work into a PDF file does not make it "published". But hey, don't believe me, the policy and guideline pages explain it better than I do - that's where I get it all from. — Cheers, Steelpillow (Talk) 18:42, 2 February 2015 (UTC)[reply]

To be fair we do live in a strange universe, where 4D convex uniform polytopes are mostly identified over a 100 years ago, and enumerated complete in the 1960's and nothing published in detail, unpublished manuscripts referenced in papers in the 1990's, and webpages put up in the 1990's are referenced by 2004 PhD dissertation proving the list complete. Even now, if you ignore Olshevsky and Klitzing, there are ZERO clear sources that actually list all convex uniform 4-polytopes with element types and counts. Conway's 2008 book skims through all the truncated forms, using the 120-cell family for example with vertex figures and partial honeycomb pictures, but otherwise doesn't give a single count for how many elements. If we scanned everything from Coxeter we'd have a patchwork of incomplete information given as examples and that would be unpresentable. My pessimism on sources that would meet your standards might be incorrect, but I think unless we can get a "seal of approval" of some sort for Olshevsky and Klitzing's work, even partial work, we might as well stick needles into our eyes and wait for god to make us see again. Tom Ruen (talk) 19:07, 2 February 2015 (UTC)[reply]

That's the way it works in here. I would reiterate, they are the Wikipedia community standards not mine. If you want to do things a different way, there is a whole wide world of web sites out there waiting for you. It would save you the price of a packet of needles, and who knows if the citations mount up you might become a reliable source yourself one day. For my part I reckon I'm about half way there, with four peer-reviewed essays to my credit but so far my web site has only been cited on a different subject altogether. — Cheers, Steelpillow (Talk) 19:16, 2 February 2015 (UTC)[reply]

So if Norman Johnson wrote a paper outlining the contents of his unpublished book on uniform polytopes, and referenced Klitzing's webpage listing of 3D uniform honeycombs as (complete as known), 4D convex uniform polytopes as proved complete, and 5D as "complete as known", etc., what would that accomplish in your eyes?

My understanding of Wikipedia's policy and guidelines is that once Johnson's paper was peer reviewed and published, we could at least consider referencing the paper, along with any aspects of his book (once published, not the ms) and Klitzing's site that the paper explicitly endorses, say the lists by mathematical symbol. But we could not include say edge counts unless Johnson's paper says they are correct. An even where specific material is endorsed, we would need to pay attention to things like notability and encyclopedic value. For example if Johnson says that Klitzing has named them all, a massive list of polytope names might be regarded as too much a minority sport and liable to variation by subsequent authors, for them to be used here. It might be better to wait until a standard list of names was more formally adopted, perhaps in a widely-read and cited paper or simply through an increase in third-party citations of Klitzing's list. Such borderline cases would need to be clarified through consensual discussion: first on the article talk page, then if necessary escalated to appropriate fora. But I have never seen such a paper published on this topic, only his Ph.D thesis and a lecture abstract. Has one been published? (and remember, by that Wikipedia means published through an adequate peer process) — Cheers, Steelpillow (Talk) 20:14, 2 February 2015 (UTC)[reply]

So what would you plan to call them in such a situation? Obviously you'd have to use Klitzing's names because in this scenario Johnson would have mentioned them, he is an RS, and no other names would have met those criteria. If a standard list of names was more formally adopted later then it would make sense to change them. Double sharp (talk) 10:52, 3 February 2015 (UTC)[reply]

Allow me to repeat what I just wrote, "Such borderline cases would need to be clarified through consensual discussion: first on the article talk page, then if necessary escalated to appropriate fora." I have no intention of going any further into my example discussion unless and until it enters the real world. — Cheers, Steelpillow (Talk) 11:09, 3 February 2015 (UTC)[reply]

OK, thanks for clarifying this. I don't intend to go further into these hypotheticals either, at least while they remain hypotheticals. :-) Double sharp (talk) 13:51, 4 February 2015 (UTC)[reply]

On externally linking Klitzing's site: WP:ELMAYBE #4 states that links to "[s]ites that fail to meet criteria for reliable sources yet still contain information about the subject of the article from knowledgeable sources" should be considered and not automatically rejected, so this can and probably ought to be discussed. However, material only found on his site should obviously not be presented on WP, as it doesn't (yet) qualify as a reliable source. Double sharp (talk) 15:55, 4 February 2015 (UTC)[reply]

Nor can we use this as an excuse to link to pages mixing reliable and unreliable material. — Cheers, Steelpillow (Talk) 16:52, 4 February 2015 (UTC)[reply]

Original research

It now transpirs that this article contains a good deal of original research. Tomruen (talk · contribs) 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? — Cheers, Steelpillow (Talk) 10:52, 2 February 2015 (UTC)[reply]

Shouldn't it be fine per WP:CALC? Double sharp (talk) 10:48, 3 February 2015 (UTC)[reply]

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. — Cheers, Steelpillow (Talk) 11:21, 3 February 2015 (UTC)[reply]

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)[reply]

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. — Cheers, Steelpillow (Talk) 15:06, 4 February 2015 (UTC)[reply]

I think all the basic polytopes (i.e. regulars, demihypercubes, E_n 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 (t_0,...,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)[reply]

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)[reply]

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)[reply]

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)[reply]