From Wikipedia, the free encyclopedia
Jump to: navigation, search
WikiProject Mathematics (Rated B-class, Low-priority)
WikiProject Mathematics
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
B Class
Low Priority
 Field: Geometry

stub and definitions[edit]

I started this as a framework for expansion in enumerating known polytopes of varied dimensions, but I'm unsure how much I can get done in 5 days! I can move it to a user subpage until I've got it fleshed out if that is better. Tom Ruen 19:10, 4 September 2006 (UTC)

My major concern is that "Polyteron" and friends don't appear in any reliable sources I find find. If they're neologisms being promoted only through a few personal webpages on the Internet, we don't need to repeat them! Melchoir 19:43, 4 September 2006 (UTC)
I made parallel pages like 5-polytope as redirects. I can move the content to those pages instead and reference objects with ugly names like hexa-5-tope over hexateron. I figured a systematic scheme used by actual researchers into these forms is worth something. So if Norman Johnson finally gets his book Uniform Polytopes published using these terms, then all is well? Tom Ruen 19:57, 4 September 2006 (UTC)
Well, if the existing literature uses ugly names (and agreed, they're ugly names), we ought to be using the same ugly names. If a published source arises, like Johnson, then of course we can choose to follow it. Melchoir 20:32, 4 September 2006 (UTC)
Polyteron and later are of my invention. While there are indeed words like 'hexa-5-tope' and 'pentatope', these put two numbers in apposition, which makes it hard to break when one number runs onto another (icosa-tetron = 20 * 4tope or 24-tope). The use of metric prefixes in this way overcomes the problem, since these are meant to stand beside these numbers. Wendy.krieger 09:54, 19 September 2007 (UTC)
I do not especially like 'polyteron,' etc. polyktirio (poly-building) or one based on the Greek word for 'house' would be better. Polychoron means room, so when they are in something higher they can be a room in something: there is no reason to start using numbers and making it less intuitive.
The term "polyteron" should not be used in this article if it's a self-invention of editors or hobby-mathematicians (George Olshevsky). I've started replacing the word by the "official" term 5-polytope... --Roentgenium111 (talk) 23:49, 4 May 2010 (UTC)
...finished. Though this should be done systematically for all related articles...--Roentgenium111 (talk) 19:01, 7 May 2010 (UTC)


I copied the definition section from polychoron, upgrading the dimensions.

I'm not sure I'm content with #2: Adjacent hypercells are not in the same four-dimensional hyperplane.

Perhaps this criterion is a way to separate polytopes from tilings. It may be a definition for a convex polytope, but not a general polytope!

I'll put a note in talk for polychoron as well. Tom Ruen 01:11, 4 September 2006 (UTC)

Uniform 5-polytopes (polyterons)[edit]

I've got an in-progress complete table at User:Tomruen/uniform polyteron (In parallel form as tables of Uniform polychoron). Tom Ruen (talk) 18:24, 20 November 2007 (UTC)


I removed this. I couldn't find any reference where it was used and no reference offered. (so far!) Tom Ruen (talk) 03:54, 6 June 2008 (UTC) Another proposed name is polyktiria ('many house,' as polychoron is 'many room.')

I propose it: I have more than a minor in math.--Dchmelik (talk) 06:44, 6 June 2008 (UTC)
An encyclopedia is not where you propose names for things... It would do wonders for the usefulness of this (and similar pages) if made-up words were reduced to the ideal minimum of zero! Mariano (talk) 13:55, 6 June 2008 (UTC)

Section "Notes on the Wythoff construction for the uniform 5-polytopes"[edit]

Why in the table in right column is "Any regular 4-polytope" but not "Any regular 5-polytope"? And similar to the bottom. Maksim-e (talk) 19:53, 8 October 2008 (UTC)

Typos from copying. Thanks! Tom Ruen (talk) 21:52, 8 October 2008 (UTC)

In the table, line "Truncated": "Each original vertex is cut off, with a new face filling the gap." -> "Each original vertex is cut off, with a new facet filling the gap."? Maksim-e (talk) 10:43, 11 October 2008 (UTC)

Ambigious definition[edit]

does not intersect itself looks ambiqious...

Vertex intersects with edge? Edge intersects with face? Jumpow (talk) 21:46, 15 February 2016 (UTC)

It says this for convex cases "...its boundary (including its cells, faces and edges) does not intersect itself" The boundary is made of cells, faces, edges, and vertices. If any two elements intersect each other its not, convex, like a pentagram is self-intersecting, edges intersect each other. Tom Ruen (talk) 21:51, 15 February 2016 (UTC)
More accurately, polytope terminology uses the idea of incidence of the elements rather than their intersection. Incidence is closer to the geometrical idea of tangency than of intersection: a vertex is incident with an edge, an edge is incident with a face. The term "intersection" is used only for the object as a whole. For a face and one of its edges to actually intersect, the face has to be a star polygon, which is self-intersecting. To explain all this every time convexity is briefly explained would make such articles tedious. Rather, we accept that one of the possible meanings is mathematical nonsense as you observe, while the other makes sense: as is very common in English prose, we credit the reader with the intelligence to reject the nonsensical interpretation. HTH — Cheers, Steelpillow (Talk) 08:43, 16 February 2016 (UTC)
Thank you. I undestood... Keyword there is itself, separately from other elements. Jumpow (talk) 17:31, 16 February 2016 (UTC)