The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.

The result was delete. There is at least consensus to delete the polygons explicitly nominated here. Which (other) polygons should have articles or redirects is beyond the scope of this AfD and can continue to be discussed in an appropriate location if need be. Sandstein 10:26, 3 October 2018 (UTC)[reply]

180-gon (edit | talk | history | protect | delete | links | watch | logs | views) – (View log · Stats)

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Not a notable shape; no references or claims of importance (the Wolfram link doesn't mention this specific polygon). This has been created and redirected several times; posting to AFD to get a clear consensus. power~enwiki (π, ν) 22:02, 25 September 2018 (UTC)[reply]

I am also nominating these other articles on polygons with large numbers of sides and no references:

• 144-gon (edit | talk | history | protect | delete | links | watch | logs | views)
• 240-gon (edit | talk | history | protect | delete | links | watch | logs | views)
• 720-gon (edit | talk | history | protect | delete | links | watch | logs | views)

• Comment Icosihenagon, Icositrigon, Triacontahexagon, Tetracontapentagon, and Heptacontadigon should also be added as additional (re)creations by the same editor without claims of significance or references. Double sharp (talk) 01:20, 26 September 2018 (UTC)[reply]
• Delete 144-gon, 180-gon, 240-gon, and 720-gon as they have no references or claims of significance, and we can't go around having redirects for every possible number of sides. Redirect Icosihenagon, Icositrigon, Triacontahexagon, Tetracontapentagon, and Heptacontadigon to List of polygons; they're also non-notable, but they follow an accepted naming system up to 99 sides, and it's plausible that readers might search them given that quite a few articles exist for polygons with numbers of sides between 21 and 100. Double sharp (talk) 01:20, 26 September 2018 (UTC)[reply]

I think all polygons up to 24 sides should have their own articles, 24 is a better place (than 20) to stop at. Thus, I create articles for all polygons up to 24 sides (also create redirects for all polygons with odd sides 25<=n<=36, since all polygons with even sides 25<=n<=36 already have their own articles, all odd sides 25<=n<=36 (icosipentagon, icosiheptagon, icosienneagon, triacontahenagon, triacontatrigon, triacontapentagon) redirect to List of polygons#List of n-gons by Greek numerical prefixes, and 25-gon, 27-gon, 29-gon, 31-gon, 33-gon, 35-gon redirect to polygon. However, most n>=37 are still red links, and I think 36 is enough, we should not have redirects for n>=37). Besides, I think all polygons with number of sides divides 720 also should have their own articles, since their angle is multiple of 0.5 degrees. --- Xayahrainie43 (talk) 09:41, 27 September 2018 (UTC)[reply]

I also create redirects for other name of polygons: If the polygon has its own article, then redirect to this article (e.g. septagon redirects to heptagon, hexdecagon redirects to hexadecagon, the only exception is trigon, which redirects to a disambiguation page), if the polygon doesn't have its own article (only for n<=36 and n=100*k with k<=9), then redirect to List of polygons#List of n-gons by Greek numerical prefixes (e.g. all of icosikaipentagon, icosapentagon, icosikaiheptagon, icosaheptagon redirect to List of polygons#List of n-gons by Greek numerical prefixes) --- Xayahrainie43 (talk) 09:39, 27 September 2018 (UTC)[reply]

• delete the numerically named polygons, redirect the rest (though I see some have been taken care of already). No indication of independent notability, no sources indicating any, anything that can be written about them is just the general properties for an n-gon with n set to 180, 144, 240 etc. No policy-based rationale given for having them or keeping them in Xayahrainie43's comment above. An editor’s personal preference is not a reason – see WP:ILIKEIT.--JohnBlackburne^words_deeds 08:37, 26 September 2018 (UTC)[reply]

First, why we stop at 20? Not 24? I think 24 is a better place to stop at. Second, why 120 and 360 can have their own articles but 144, 180, 240 and 720 cannot? All of them are divisors of 720, especially 240, all divisors of 240 except 240 itself already have their own articles. Third, all even number up to 34 have their own articles, but why can't 36 have? 36 is important since it is a divisor of 720 and its angle is 170 degrees. --- Xayahrainie43 (talk) 09:24, 26 September 2018 (UTC)[reply]

• Delete No apparent reason for creating these articles and with no indication of notability. Fails WP:GNG. Hzh (talk) 13:30, 26 September 2018 (UTC)[reply]
• Comment It strikes me that some more of these polygons in addition to those created by Xayahrainie43 are also not notable. I have in mind icosidigon (22), icosihexagon (26), and icosioctagon (28). While all of them have references, the references appear to be only general ones describing some relationships that some 2n-gons have to n-gons. While I have no objections to presenting this information when the 2n-gon is notable for other reasons, such as for icositetragon (24) and triacontagon (30), I don't think it's sufficient to make it notable by itself when there's nothing else to say. Everything written on the 22-gon, 26-gon, and 28-gon in their articles can be ported straight to any other even-sided regular polygon; just change the numbers. Hence I think they should be redirected as well. While it's useful to have a variety of small cases illustrated, we already have so many even-sided polygons with articles that I think the point has been made already and we don't need these extra three.
• Among the polygons with over 20 sides: a standard form of the prefix that is commonly agreed on would be one thing; an explicit construction (even if not classical) or at least a non-trivial closed form of the trigonometric functions in the formulae would be one thing; a historical appearance would also be one thing, as would some mathematically significant properties. These are all claims of significance and give information that has a real reason to appear outside list of polygons. I would think that {24}, {30}, and {42} pass the "mathematically significant" test; {48} and {96} pass the "historically significant" test (because of Archimedes); {32}, {34}, {40}, {60}, {64}, {80}, and {120} pass the "trigonometric expressions can be expressed in non-trivial real radicals" test; {50}, {70}, {90}, and {100} pass the "commonly agreed-on name that gives an unbroken set of tens" test; and {257} and {65537} are outstandingly notable in mathematics just as {1000}, {10000}, and {1000000} are notable in philosophy. Granted, writing a complete article about any of them necessitates including some boilerplate but true properties that can be varied for any n-gon; the important thing is that these values of n have some other things to say about them that combined with the boilerplate text actually produces a real article. Already 360-gon is almost not a real article (everything in it can be ported straight to other n-gons), and the only thing interesting about it is that it corresponds exactly to degrees (which would probably lead to something, as approximate constructions of 1° angles seem like something that could be found elsewhere). I don't think you'd find even that for the other integer-degree polygons, much less a 21-gon or a 23-gon, so I'd draw the line after {360}. So I think we could use a bit more pruning: perhaps not only 21, 23, 36, 45, and 72 should be redirected, but also 22, 26, and 28. (Pinging Tomruen as he converted those three to articles; I was also involved in turning some of these into articles back in 2015, but I would like to think that they were for the most part the more notable ones). Double sharp (talk) 14:22, 26 September 2018 (UTC)[reply]

Well... I think 240 also pass the "trigonometric expressions can be expressed in non-trivial real radicals" test. After all, all divisors of 240 except 240 itself already have their own articles. --- Xayahrainie43 (talk) 18:00, 26 September 2018 (UTC)[reply]

Obviously there must be some limits, or else we could go out and write up a trivial article on the 16777216-gon. While a 240-gon does have this property, it doesn't even have a standard name. (257 and 65537 as the base cases for those Fermat primes are one thing, but after 120 the point is made already; in fact one could easily argue that it's been made by the time you get to the 30-gon or 60-gon already). So I intended this sort of criterion to apply for the polygons between {21} and {100} which have reasonably standardised names but don't necessarily have enough to demonstrate notability. Indeed 120-gon and 360-gon are rather weaker than the others. I've gotten rather more deletionist on these since I created those two in 2015 as part of the series, as while those have at least a potential claim (prefix forms for 120 and the approximate construction of a 1° angle for 360), they are quite weak. I'd be happy cutting things down to {24, 30, 40, 42, 48, 50, 60, 70, 80, 90, 96, 100, 257, 1000, 10000, 65537, 1000000} or even further (since {32} and {64} only have constructability to claim for themselves, and {34} follows immediately from {17}). Double sharp (talk) 03:24, 27 September 2018 (UTC)[reply]

Well, but ALL divisors of 240 except 240 itself already have articles... Besides, I think 24 (rather than 20) is a better place to stop at, beyond 24 I suggest {30, 32, 34, 40, 42, 48, 50, 60, 64, 70, 80, 90, 96, 100, 120, 240, 257, 360, 1000, 10000, 65537, 1000000, ∞} but not {26, 28, 36, 45, 72, 144, 180, 720} (see below) --- Xayahrainie43 (talk) 05:29, 27 September 2018 (UTC)[reply]

So? All divisors of 192 but 192 itself also have articles, but that doesn't by itself make the regular 192-gon notable. Double sharp (talk) 10:18, 27 September 2018 (UTC)[reply]

Also, I think 24 is the better (than 20) place to stop at, for polygons with over 24 sides: a standard form of the prefix that is commonly agreed on would be one thing; an explicit construction (even if not classical) or at least a non-trivial closed form of the trigonometric functions in the formulae would be one thing; a historical appearance would also be one thing, as would some mathematically significant properties. --- Xayahrainie43 (talk) 18:01, 26 September 2018 (UTC)[reply]

Besides, the polygons (according to my edit) should have articles are: (these numbers are listed in my edit [1])

• n <= 24
• n even and n <= 36
• n = 2^k where k <= 6
• n divides 720
• n = 42
• n = 96
• n = 10*k where k <= 10
• n = 2^(2^k)+1 where k <= 4
• n = 10^k where k <= 4 or k = 6
• n = ∞

and the polygons should have redirects are: ("n-gon" redirects to polygon, and the name of n-gon (e.g. icosipentagon) redirects to List of polygons#List of n-gons by Greek numerical prefixes):

• n odd and 25 <= n <= 36
• n = 100*k where 2 <= k <= 9

--- Xayahrainie43 (talk) 18:06, 26 September 2018 (UTC)[reply]

In fact, only 14 polygons should have redirects: 25, 27, 29, 31, 33, 35, 200, 300, 400, 500, 600, 700, 800, 900. --- Xayahrainie43 (talk) 05:20, 27 September 2018 (UTC)[reply]

It all seems pretty harmless. Certainly triacontagon (30) is important since it is the highest petrie polygon in 4 and 8 dimensional polytopes. Tetracontadigon (42) is the highest regular polygon that can fill a point with other regular polygons. And constructible polygons are also important. Tom Ruen (talk) 20:41, 26 September 2018 (UTC)[reply]

Yes, 30 and 42 are important, an n-gon with n > 24 should be included if and only if a standard form of the prefix that is commonly agreed on would be one thing; n-gon is an explicit construction (even if not classical) or at least a non-trivial closed form of the trigonometric functions in the formulae would be one thing; a historical appearance would also be one thing, as would some mathematically significant properties. Thus 30, 32, 34, 40, 42, 48, 50, 60, 64 should be included, but 25, 26, 27, 28, 29, 31, 33, 35, 36 should not. --- Xayahrainie43 (talk) 05:18, 27 September 2018 (UTC)[reply]

• Delete. Not independently notable. No interesting properties that are not shared by other n-gons (having an integer number of degrees per angle is not an interesting property). Fails WP:NUMBER and WP:GNG. —David Eppstein (talk) 22:02, 26 September 2018 (UTC)[reply]

All polygons with <= 24 sides should be included, for polygons with over 24 sides:

• 30 and 42 pass the "mathematically significant" test
• 48 and 96 pass the "historically significant" test (because of Archimedes)
• 32, 34, 40, 60, 64, 80, 120, and 240 pass the "trigonometric expressions can be expressed in non-trivial real radicals" test
• 50, 70, 90, and 100 pass the "commonly agreed-on name that gives an unbroken set of tens" test
• 26, 28, and 36 (with even sides <= 36) can also be included
• 45, 72, 144, 180, 360, and 720 pass the "have the number of degrees per angle divisible by 0.5" test
• 257 and 65537 are notable in mathematics
• 1000, 10000, and 1000000 are notable in philosophy
• ∞ is also notable as limits.

They are exactly the polygons in [2], red numbers (with the exception of 360) I think can be deleted now. --- Xayahrainie43 (talk) 05:03, 27 September 2018 (UTC)[reply]

Also suggest to remove the redirects tetracontatrigon (43-gon) and henkaipentacontagon (51-gon, not a name in the list in List of polygons#List of n-gons by Greek numerical prefixes) to List of polygons#List of n-gons by Greek numerical prefixes, polygons with > 36 sides (except 100*k sides with 2<=k<=9) should not have redirects to List of polygons#List of n-gons by Greek numerical prefixes. --- Xayahrainie43 (talk) 09:27, 27 September 2018 (UTC)[reply]

I added the article 4294967295-gon, since it may be the largest constructible polygon with an odd number of sides. --- Xayahrainie43 (talk) 10:02, 27 September 2018 (UTC)[reply]

Please provide sources to support claims of notability. We in Wikipedia are not interested in assertions about notability, but notability that can be demonstrated by the existence of multiple independent reliable sources per WP:RS that discuss that subject in depth. If sources are not forthcoming, then the articles may be deleted. Hzh (talk) 10:38, 27 September 2018 (UTC)[reply]

Note: This discussion has been included in the list of Mathematics-related deletion discussions. Coolabahapple (talk) 13:09, 29 September 2018 (UTC)[reply]

The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.