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Template talk:Polytopes

old commentsEdit

For all the entries except 2-4, the names constitute original research, and the redirect for 1- is inappropriate. The template makes sense, but the names should be revoked. I don't want to, even temporarily, damage the template by putting the appropriate {{or}} tags inside, but something needs to be done. — Arthur Rubin (talk) 16:11, 8 February 2010 (UTC)

OK, I enclosed the {{or}} tags in noinclude tags, so that the resultant articles aren't tagged as being OR. If this isn't resolved soon, I may propose the template for deletion. — Arthur Rubin (talk) 16:30, 8 February 2010 (UTC)
I changed the links to n-polytope, removed 1-polytope. Tom Ruen (talk) 02:02, 9 February 2010 (UTC)
They're not original research, they're suggested names. But they probably aren't notable enough. I suggest using polychoron but not the higher ones, as the article for 4-polytopes is at polychoron. 4 T C 06:15, 9 February 2010 (UTC)
They're original research, unless the names were suggested in a reliable source. (They don't need necessarily to be suggested by a reliable source, just in a reliable source.) — Arthur Rubin (talk) 08:50, 9 February 2010 (UTC)

new versionEdit

I think we can borrow details from this table

Fundamental regular and uniform polytopes in dimensions 2-10
1k2, 2k1, k21
F4 Hn
2 triangle
Square x x x Pentagon
3 Tetrahedron
x x Dodecahedron
4 5-cell
x 24-cell 120-cell
5 5-simplex Penteract
Demipenteract x x x
6 6-simplex Hexeract
Demihexeract 122 221 x x
7 7-simplex Hepteract
Demihepteract 132 231 321 x x
8 8-simplex Octeract
Demiocteract 142 241 421 x x
9 9-simplex Enneract
Demienneract x x x
10 10-simplex Dekeract
Demidekeract x x x


Mateus Zica (talk) 23:45, 11 February 2010 (UTC)

I made it a bit more compact, removed less important elements.Tom Ruen (talk) 00:28, 12February 2010 (UTC)

Option 1Edit


i made a new simplier version Mateus Zica (talk) 15:51, 12 February 2010 (UTC)

Looks good! (except x's) Tom Ruen (talk) 21:16, 12 February 2010 (UTC)
More improvements in layout
Mateus Zica (talk) 08:52, 14 February 2010 (UTC)

Option 1 : New VersionEdit

New version :

  • Separated columns for n-HyperCube and n-Orthoplex
  • Separated columns for 1k2 , 2k1 and k21
It looks good. You can just add to the template directly, no need for waiting for feedback on small changes. :) Tom Ruen (talk) 03:53, 20 February 2010 (UTC)

Mateus Zica (talk) 14:11, 19 February 2010 (UTC)


Option 2Edit

From User:4 (including star polytopes)

Option 3Edit

From User:Tomruen (Variation of option 2 format, but focus on groups)


I listed 3 tables above, no strong preference by me. Partly it depends on where it'll be used. Categorical articles ought to have catagorical navigators perhaps, and individual articles have individual navigators by the group!? Tom Ruen (talk) 04:25, 14 February 2010 (UTC)
I think option 3, removing the suggested names, seems reasonable. I don't think penteract (for 5-cube) has any more sourcing than polytera (for 5-polytope), but I don't feel like nominating the entire set for deletion. — Arthur Rubin (talk) 04:26, 15 February 2010 (UTC)
I changed the names in option one to the n-XXX style, and just n-polyope in last table. SO the first table has "single-end-ringed polytopes" by symmetry group, the second table has the same PLUS regular nonconvex regulars. The third table has groups of polytopes. I'd lean towards the FIRST table for a navigator of that SET of polytopes (Call it Template:Quasiregular_polytope for lack of a better categorical name), and the third option for the n-polytope and listed grouped polytope families under this template. Tom Ruen (talk) 22:14, 15 February 2010 (UTC)
I replaced the template with "option 1" since it seemed the best "map" of the polytope families as this template is used within the uniform polytope articles. Perhaps it should be RENAMED to something else, if there's a more general usage for "Option 3"? Tom Ruen (talk) 07:47, 17 February 2010 (UTC)

Too bigEdit

Looking at it now after the changes by User:Yaoliding it is much too wide: somewhere around 1400 px with my default, very small, font size. The point of a navigation template is navigation. The extra names should be handled in the articles or, if they are common enough that they might be searched for, in redirects.--JohnBlackburnewordsdeeds 13:44, 25 March 2010 (UTC)

Thanks, I'll try to edit it in the right way (I'm not good at speaking English, I hope I didn't make some grammar error). By the way, is it right to add something likes F2 and E3 polytope in the Template?—Preceding unsigned comment added by Yaoliding (talkcontribs) 14:19, 26 March 2010 (UTC)
As you can see User:Arthur Rubin has already done the bold thing and reverted your changes. It's already a very large template so I would try to only add things that do not make it bigger, i.e. fill in gaps if you can, or use better names if they are not too long. It's a navigation template so does not need all name variations listing - users can find those out by going to the articles. And too much information just obscures what's there and confuses people.--JohnBlackburnewordsdeeds 14:37, 26 March 2010 (UTC)
The question of whether it's F4 or Fn, and Gn or GHn, are substantive questions which may be worthy of discussion. It's been so long since I looked at the Lie groups in question, that I'm not sure which is correct. The full names, even if, (IMHO) by mistake, the article is at penteract rather than at 5-cube, 5-cube is better in the template. — Arthur Rubin (talk) 21:48, 26 March 2010 (UTC)
I have just made some changes, I make a smaller template now, though it is still very big :( , and I hope there is no mistake in it. I think penteract is better than 5-cube, after all penteract is more professional, and almost of us have known which deminsion some polytopes is.

────────────────────────────────────────────────────────────────────────────────────────────────────Again there are problems with the recent changes, for example

  • Redlinks and external links. As per WP:NAVBOX links should be to existing articles only, so no red links and no external links, even to image pages.
  • Some of the additions are not polytopes but are lattices, points and lines.
  • Some are just duplicates of other links, e.g. to Square.
  • I don't think changing names from e.g. 5-cell to Hexateron helps: the former is clearer, and some of the new names are not even well established names but OR: see the top of this page.

More generally there's a problem with the number of edits and lack of edit summaries. If you want to edit an article please use the preview button to see your changes before submitting them, rather than only checking after submitting, and provide proper edit summaries to explain what your changes are.--JohnBlackburnewordsdeeds 13:14, 27 March 2010 (UTC)

The redlinks have gone but

  • (Again) links should be to existing articles only, so no unlinked names: if important they should be explained in articles.
  • It's too wide again, due to the longer names and a totally redundant extra column which is has just a spare link to Regular polygon using a name "p-gon" not used at all in the article.

--JohnBlackburnewordsdeeds 15:16, 27 March 2010 (UTC)

Wow, thanks for your suggestion at first.
Most of the links which I add doesn't exist in the article, I know. Such as E2,E3,F2, they're the result which I derived (So I'm worried about if I make some serious errors.), I think maybe they (E2,E3,F2...) is not important in Uniform Polytopes, then we ignore them. So I try to add them in the template.
The group “I2(p)” and “p-gon” is just copied from Coxeter Group. It isn't a problem, I think. —Preceding unsigned comment added by Yaoliding (talkcontribs) 15:48, 27 March 2010 (UTC)
A "result which I derived" is original research and so not allowed. "p-gon there makes sense because of the p in the other columns. It is shorthand for "the polygon with p edges" not another name for "regular polygon". But it doesn't really address the other issues, of the confusing name changes, the extra width, unclear duplicate links, and the many things that are not polytopes.--JohnBlackburnewordsdeeds 15:58, 27 March 2010 (UTC)

Oh...So, is it wrong to add "p-gon" and the others in the templete? I wish you can help to edit according your opinion. After all, it;s very difficult for me to read and express in English. Sorry. —Preceding unsigned comment added by Yaoliding (talkcontribs) 16:12, 27 March 2010 (UTC)

Seems I was wrong before, but I don't understand, Doesn't some groups like E3 and F2 exist? —Preceding unsigned comment added by Yaoliding (talkcontribs) 11:43, 31 March 2010 (UTC)
I don't think E3 and F2 have polytopes associated. I wouldn't have reverted those without study, if you hadn't also used odd, long, names for the polytopes. Tesseract is standard, but I'd argue that Penteract should redirect to 5-cube, rather than the other way around. — Arthur Rubin (talk) 15:58, 31 March 2010 (UTC)
I don't understand, why to use 10-simplex and 10-cube but not their full names. It doesn't look beautiful, I think. Maybe I should turn the template back to Option 1 New Version completely. And I think using F4 is better than Fn if we delete the F2(square).
Actually, I think all simplecies (sp?) and cubes over dimension 4 should use the standard name n-simplex, n-cube, and n-cross polytope. None of the other names have much weight in the real world. Agree with Fn to F4, as F2 is one of the other groups (B2?). — Arthur Rubin (talk) 17:15, 3 April 2010 (UTC)
As an aside, how does one do a bulk rename request:
  • Hexateron to 5-simplex
  • Heptapeton to 6-simplex
  • Octaexon to 7-simplex
  • Enneazetton to 8-simplex
  • Decayotton to 9-simplex
  • Pentacross to 5-orthoplex
  • Hexacross to 6-orthoplex
  • Heptacross to 7-orthoplex
  • Octacross to 8-orthoplex
  • Enneacross to 9-orthoplex
  • Decacross to 10-orthoplex
  • Penteract to 5-cube
  • Hexeract to 6-cube
  • Hepteract to 7-cube
  • Octeract to 8-cube
  • Enneract to 9-cube
  • Demipenteract to 5-demicube
  • Demihexeract to 6-demicube
  • Demihepteract to 7-demicube
  • Demiocteract to 8-demicube
  • Demienneract to 9-demicube
 ? — Arthur Rubin (talk) 17:39, 3 April 2010 (UTC)

────────────────────────────────────────────────────────────────────────────────────────────────────You can just post them to WP:RM, which has instructions and a couple of examples. Or you could just move them: there's no requirement if it's a relatively uncontroversial move.--JohnBlackburnewordsdeeds 17:49, 3 April 2010 (UTC)

I'm afraid both the current polytope-naming editor and the previous polychoron-naming editor would disagree; it's relatively uncontroversial, but that's two non-vandal editors who would have an honest disagreement. — Arthur Rubin (talk) 17:56, 3 April 2010 (UTC)
Correction to part of the above, I wrote n-cross polytope, while Coxeter used n-orthoplex. "Cross polytope" is the correct generic term, but 5-orthoplex seems to have more usage than 5-cross-polytope. — Arthur Rubin (talk) 18:01, 3 April 2010 (UTC)
I think n-orthoplex means k11 polytopes and it should belongs to Dn group (n-demicube is 1k1). So I think use n-cross is better, it has the same Coxeter-Dynkin diagram as n-cube.
While there is a new problem, in Uniform polytope, I see they use [3k,1,1] but not [3n,4] to express Bn polytope (Cross-polytope). Is it Wrong? Why they doesn't use [3n,4] to express Bn polytope?
P.S. Square is belong to both BC2 and F2 group, but F2 doesn't seem to be necessary and important, so we ignore it. And use n-cube is better n-hypercube, I think.
I have just made a much more complex version.Are there any inadequates or errors in it? Yaoliding (talk) 09:25, 13 June 2010 (UTC)

Added G2Edit

I regrouped the Exceptional Lie_groups together in one column, and this allowed G2 to be added. I didn't know Hn Coxeter groups are not included as Lie groups, apparently because they can't tessellate space. So I linked all the group titles, except Hn at the end! Tom Ruen (talk) 01:46, 2 December 2010 (UTC)

Sorry, I think something is wrong in the template

Although G2, F4 and E6~E8 are Exceptional Lie groups, but these three groups have a lot of difference, they don't have the simple connection. It's inappropriate to put them in the same column. Er...By the way, why the line "n-polytope" was in the bottom of the form? Actually the polytope of E2,E3,E4,E5 is in exist(F2 as well), even they are not exceptional Lie groups。 —Preceding unsigned comment added by Yaoliding (talkcontribs) 05:20, 5 December 2010 (UTC)

It was an aethetic decision, based on the fact there's only one G2, one F4, and seemed wasteful to have columns devoted to them. Previously G2 was skipped completely. Shared space risks confusion, but I hoped the blank dimensions would help. (Perhaps shading background colors differently might help a bit more?) It's less of a problem on table width here, than Polytope families which uses the same columns, and they need to be a bit wider with graphs included. Tom Ruen (talk) 05:46, 5 December 2010 (UTC)
en. Well, what about the classification of each column? I think Hexagonal tiling is stand for G3, and it's in exist. There is only one convex polytope in G group, it have no special convex polytope, so we often use I2(6) instead G2, as well as to use BC2 and I2(4) instead F2

Regular polygons?Edit

I added an In(p) column to the template. Also, I was wondering if something like Schläfli symbols or Coxeter-Dynkin diagrams would be a good thing to include or if it would make the template too cluttered. Aacehm (talk) 19:54, 13 December 2011 (UTC)

It was removed a couple months ago. The link to Polytope_families shows a similar table with graphs and CD diagrams. Tom Ruen (talk) 20:34, 13 December 2011 (UTC)
Clutter is not so much a problem as redundancy and confusion. The link to regular polygon is already there, without which the column is empty, and the name isn't piped which makes it much easier to find, the whole point of a navigation box. This is even more of a problem with the heading as the article it links to isn't "In(p)" and doesn't mention it. Anyone following that link to find out what In(p) stands for is going to be very confused.--JohnBlackburnewordsdeeds 20:56, 13 December 2011 (UTC)
I noticed that In(p) isn't really mentioned on Wikipedia other than briefly under Coxeter group, which would also be confusing if linked to. Is there any way we could provide more information on it? I was thinking about putting it into Simple Lie group but I'm not quite sure if it could go there. Other groups (An, BCn, etc.) are mentioned, but they don't have their own articles. Are they not "exceptional" enough? ;-) Aacehm (talk) 01:04, 14 December 2011 (UTC)
Yes, it looks like only the Exceptional simple Lie groups have individual articles: G2, F4, E6, E7, and E8. Tom Ruen (talk) 01:40, 14 December 2011 (UTC)
Do you think the other Lie groups should have their own articles? Double sharp (talk) 14:41, 14 April 2012 (UTC)

Calculator and questionEdit

Hi guys. I started this question on Quora:

And this calculator on Google Sheets:

They are good points to help the improvement of this article. The table could be expanded to help comparision between all shapes.--TudorTulok (talk) 22:15, 12 October 2014 (UTC)

I looked at the second link. I have no interest in making an account on Quora. The simplex, hypercube, and orthoplex articles have tables for each polytope family. This table is intented as a compact navagator. Tom Ruen (talk) 05:02, 13 October 2014 (UTC)
Return to "Polytopes" page.