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Mathematics C‑class Top‑priority

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Archive 1

This page has archives. Sections older than 365 days may be automatically archived by Lowercase sigmabot III when more than 4 sections are present.

Polyhedrons and polytopes as polygons

AxelBoldt removed the statement:

Strictly speaking, every polyhedron is also a polygon as is every polytope, since they all have angles.

with the simple claim:

Polyhedra are not polygons.

Since it is obvious that polyhedron have multiple angles, and hence are polygonal, I'd like to give him a chance to explain why he removed true information.

Simple: because it's not true at all. "Polygon" is almost universally defined as a 2-dimensional figure. I don't know of any mathematics text or course that treats it as a superclass that includes 3-d polyhedra. Terms here should be used as they are commonly used in academia. --Lee Daniel Crocker

Lee,

perhaps you would like to suggest what term should be used for the class of objects that have multiple angles, regardless of the dimentionality? Then we could put in a reference to that class of objects in this article.

I had never heard the term polytope before I got involved with Misplaced Pages. Does the concept of the angle between two planes make sense? I, admittedly, have found very little accessible material on these topics. -- BenBaker

Maybe a phrase such as:

Even though strictly speaking, every polyhedron has multiple angles, as does every polytope, they are not considered as polygons as the angles between their faces are not two dimensional. They can be classified as 'technical-term', however.

"Polytope" is the general term, although it is typically only used to refer to 4-d and higher figures (because the 2- and 3-d figures already have names). It is, nonetheless, proper to refer to polygons and polyhedra as subclasses of polytopes. --LDC

Mathematical terms are not defined etymologically. "Polygon" may mean "many angles" in Greek, but that doesn't mean that anything with many angles is called a polygon in mathematics (and yes, you can have angles between planes). Polygons are two-dimensional figures that enclose an area with straight lines. We could have links to polytopes and polyhedra I suppose. --AxelBoldt

I am not aware of any word in any context that is defined by its etymology. Words mean whatever they are defined to mean, regardless of where they happen to come from. Adding an explicit statement to that effect in this article would be silly, because that's just a case of understanding the nature of the English language and has nothing to do with polygons. This article is about polygons, which are flat. Now, if you want to add some statement to the effect that polygons are the two-dimensional instance of the more general class of polytopes, that's entirely appropriate. --LDC

"Words mean whatever they are defined to mean, regardless of where they happen to come from." -- Indeed. That's the Humpty Dumpty argument! (Through the Looking-Glass)

On the dimension issue, it might be fair to mention that a polygon is a 2D polytope, but it's not terribly interesting. The question of a "broken" polygon in higher dimensions -- ie a set of non-planar points joined by a closed, simple path -- is perhaps interesting, but completely breaks the definition of a polytope as a convex hull of point, and there's no longer any notion of area or volume. I suppose then it's merely a path. -- Tarquin

"circulated"?

its vertices, listed in order as the area is circulated in counter-clockwise fashion,

Is "circulated" the right verb here? AxelBoldt 21:48, 26 Sep 2003 (UTC)

Vfd consensus

What is the Vfd consensus of the polygon articles put on Vfd about a week ago?? Has it been reached yet?? Georgia guy 20:27, 18 Feb 2005 (UTC)

icosa or icosi as prefix

in't the prefix for 20-side polygons icosi, as suggested on mathworld and all over the internet?

Simple Polygon

See also http://en.wikipedia.org/Talk:Simple_polygon

-- sumthinelse

"900-gon" listed at Redirects for discussion

An editor has identified a potential problem with the redirect 900-gon and has thus listed it for discussion. This discussion will occur at Misplaced Pages:Redirects for discussion/Log/2022 May 8#900-gon until a consensus is reached, and readers of this page are welcome to contribute to the discussion. 1234qwer1234qwer4 11:40, 8 May 2022 (UTC)

"120-gram" listed at Redirects for discussion

An editor has identified a potential problem with the redirect 120-gram and has thus listed it for discussion. This discussion will occur at Misplaced Pages:Redirects for discussion/Log/2022 May 8#120-gram until a consensus is reached, and readers of this page are welcome to contribute to the discussion. 1234qwer1234qwer4 12:00, 8 May 2022 (UTC)

Can We Add Names for Fake Fractional Polygons?

What's a ${\displaystyle {\frac {1}{2}}}$-gon's name? Or a ${\displaystyle 7{\frac {13}{19}}}$-gon too? We need the fractional names! Mariomaker-4 (talk) 22:23, 13 March 2023 (UTC)

Misplaced Pages is not the place for publishing or asking about neologisms and original research. And this talk page is not the place for anything other than possible improvements to the polygon article based on published references. You need to look elsewhere for your speculation. —David Eppstein (talk) 22:33, 13 March 2023 (UTC)

Maybe somewhere else? I didn't mean just on Misplaced Pages. Mariomaker-4 (talk) 22:49, 14 March 2023 (UTC)

To repeat: this talk page is not the place for anything other than possible improvements to the polygon article. Other discussion does not belong here. —David Eppstein (talk) 22:55, 14 March 2023 (UTC)

A 713⁄19-gon, Schläfli symbol ${\displaystyle \{{\frac {146}{19}}\}}$, is one of many 146-grams (the denominator can be any odd number 1<n<73). So what? —Tamfang (talk) 07:02, 17 March 2023 (UTC)

And your { 1⁄2 } is a double cover of a henagon. —Tamfang (talk) 04:33, 18 March 2023 (UTC)

Thank You! Also, can you make the page for a 146-gon? I don't want it to be a redirect. It's true name, I think, is a Hecatontetracontakaihexagon. I'll get work on the Regular Polygon db of it. It sadly won't be completely finished, but it's okay, right? Mariomaker-4 (talk) 15:16, 18 March 2023 (UTC)

NO. There is nothing to say about this polygon, specifically, that is not true of polygons in general. It is not notable, in the sense that Misplaced Pages demands for articles: there are not multiple publications that cover it in-depth, independent of other polygons. —David Eppstein (talk) 15:38, 18 March 2023 (UTC)

What if I make a... never mind. I can't even make websites! I'll ask someone else to make the page! Yeah, that's a good idea! Also, for now, it can be a redirect. Okay? I'm very sorry.  :) Mariomaker-4 (talk) 13:24, 25 March 2023 (UTC)

Didn't see my talk edit yet?I would like you to check before long. 219.104.224.225 (talk) 07:51, 19 March 2023 (UTC)

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