Talk:Regular polytope

message: I don't think it makes sense to talk about "regular polytopes in nature", unless some shape is a projection of a higher-dimensional polytope.  Otherwise, it's just "regular polyhedra in nature", and should go there instead.
We already talk about tesseracts in popular culture on tesseract.  I would be amazed if any other higher polytope arose in the media.  We also already have other pages that talk about crystals, tilings, etc. -- Walt Pohl 07:12, 17 Mar 2004 (UTC)
replies: text: Noted. mike40033 03:02, 19 Mar 2004 (UTC)

text: I plan to gradually fill in the empty sections first. Then I or you can rearrange as we see fit. mike40033 03:23, 23 Mar 2004 (UTC)
replies: text: In fact, much of the polygons and polyhedra bits are about regular symmetries rather than regular polygons/hedra. I think the whole thing needs moving to a different page - on its own or part of a more general "Polygons and polyhedra in nature", with just a few choice bits kept/repeated back here. Steelpillow 17:29, 17 January 2007 (UTC)
thread_title: Regular polytopes in nature

message: I still need a better explanation of these: is it possible to provide an illustration of a lower-dimensional analogy, such as the hemi-cube alluded to, or possibly a hemi-square to start with? --Phil | Talk 11:19, Oct 13, 2004 (UTC)
* I can try - when I get time... --mike40033 05:06, 3 Nov 2004 (UTC)
replies: text: I think the more standard name for the "banana" is a trigonal hosohedron. Double sharp (talk) 03:41, 28 February 2015 (UTC)
thread_title:  Abstract regular polytopes 

message: This article has degraded significantly due to (what appears a single editor's) concentration on theoretical vs real construction. I rm a large block that went into way too much detail on these points, but there is more yet to fix. 
There is a vast difference between the real and the ideal; what is possible in one sphere may be impossible in the other; what is impractical in the former may be essential in the latter. This page is not the proper place to open this philosophical can of worms. Regular polytope is a theoretical classification and that should be the main thrust of the article. There is certainly room for exploration of practical approximate constructions; but not here. John Reid 22:11, 27 March 2006 (UTC)
replies: text: There is always the danger of straying too far from regularity on a page like this, and especially of mistaking symmetry for regularity. For example, what are the fullerenes doing on here? Steelpillow 21:38, 16 January 2007 (UTC)
thread_title:  Approximate construction, theoretical vs real 

message: On the issue as to whether the regular star polyhedra were known before Kepler.  Jamnitzer's "great stellated dodecahedron" is sometimes offered as an example, but on close inspection its arms do not have coplanare facelets - it is a 60-faced polyhedron. One might argue for ever about the others, so I have tried to use a slightly more accurate, but non-committal, phrasing. Steelpillow 21:23, 16 January 2007 (UTC)
thread_title: Star polyhedra

message: I pointed this out in the FA review, but maybe I should put it here as well.  The current history section implicitly claims that the Greeks had a definition for, or used the term, regular polytope:
For almost 2000 years, the concept of a regular polytope remained as developed by the ancient Greek mathematicians. 
It seems unlikely to me that the Greeks had any definition at all for a "regular polytope", but I could be wrong. The article goes on to say
At the start of the 20th century, the definition of a regular polytope was as follows. ...
but no source for this definition was given, although one is needed.  Who gave this definition at the beginning of the 20th century? 
What seems to be true is that the history section describes previous discoveries that are now included in the definition of regular polytopes.  That is fine, and should be included in the article, but the wording needs improvement. CMummert · talk 14:50, 17 January 2007 (UTC)
replies: text: I agree with the thrust of what you say. To say that the Greek work applies to the concept of 'polytopes' is wrong: it applied to polygons and polyhedra. The idea of polytopes did not appear until the 19th century. Coxeter tells that Hoppe coined the term in 1882, a few decades after Schläfli had discovered some of the regular ones. So yes, some rephrasing is in order. Steelpillow 17:05, 17 January 2007 (UTC)
thread_title:  mistaken attribution of modern concepts to historic figures in history section 

message: While not disputing anything which is present in this article, it is certainly reasonable to mention a convex polytope (which many people simply call a polytope) as being the convex hull of a finite set of points. In general, these do lack all the nice symmetries of the the objects discussed in the text. However, this is a common enough object of study to deserve some mention, and at a minimum a reference to another section. Gmichaelguy 01:38, 25 April 2007 (UTC)
replies: text: Yes this is definitely worth mentioning, however polytope is probably the better article to mention this in, and indeed there is a whole section devoted to this there. --Salix alba (talk) 06:42, 25 April 2007 (UTC)
thread_title:  No mention of convex polytopes 

message: So, what does it mean to "construct[ a book] along the lines of a Bruckner symphony"? —Tamfang (talk) 03:45, 13 January 2008 (UTC)
replies: text: As far as I can recall, some of it was to do with the development of several themes a bit at a time, returning to each theme at intervals throughout the work. To make some other point Coxeter even printed a snatch of some musical score, which went waay above my head. I moved on. -- Steelpillow (talk) 22:55, 13 January 2008 (UTC)
thread_title:  I'll bite 

message: Also, we really should consider moving some of the material on this page to polytope, since a lot of it is applicable to non-regular polytopes as well.—Tetracube (talk) 22:24, 30 September 2008 (UTC)
replies: text: In general, yes. However some points on regularity will be easier to understand if a few basics on polytopes are repeated in the text. Also, the discussions for specific dimensionalities need the same treatment. -- Cheers, Steelpillow (Talk) 06:58, 2 October 2008 (UTC)
thread_title: Irrelevant material

message: When is a cube/octahedron hybrid an octahedron, as currently stated in the section on Higher-dimensional polytopes?
The thing is, the cuboctahedron is not regular. As such, it cannot easily serve as a lower-dimensional analogue of a higher-dimensional regular figure.
The figure described as a "cube/octahedron hybrid" is the 16-cell, having 16 tetrahedral cells or 3-facets and 8 vertices. I am unhappy enough about that description - where is the cube nature of the 16-cell in all this? One cannot rely on numerology alone, for different symmetries can throw up the same numbers. Here for example the symmetry of the 8 vertices in four dimensions is quite different from the symmetry of the cube's 8 vertices in 3 dimensions, despite sharing the same "8". Extrapolating that non-cubic symmetry to a "cuboctahedron" is an even greater step.
Anyway, whatever current researchers might think, I have put up a citation tag in the hope that a peer-reviewed or other equally respectable reference can be found - if not, in due course it'll have to go.
— Cheers, Steelpillow (Talk) 19:37, 18 July 2012 (UTC)
replies: text: You misread the parallel: it was cube:cuboctahedron:octahedron :: tesseract:24cell:16cell.  Still, it's sloppy language.  How do you like my rewrite?  —Tamfang (talk) 20:52, 18 July 2012 (UTC)
replies: text: OK, I get it now. I edited to try and explain even more clearly. Any good? — Cheers, Steelpillow (Talk) 20:07, 19 July 2012 (UTC)
replies: text:  Swell. —Tamfang (talk) 20:49, 19 July 2012 (UTC)
thread_title:  cube/octahedron hybrid vs octahedron 

message: Substituted at 04:06, 30 April 2016 (UTC)
thread_title: Assessment comment

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