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I made a vertex figure symmary chart on a talk subpage for reference:
Having just added a picture and some explanation, it occurs to me that it is also relevant to dual polyhedra. Should it:
-- Steelpillow 20:15, 3 June 2007 (UTC)
To quote a current snippet:
What is "imaginary" supposed to mean in this context? Perhaps "skew" is meant. And what does the construction described have to do with vertex figures? It seems quite trivial and has no real theoretical or practical significance that I am aware of. I think this should not be here, and I will delete it in a few days if nobody comes to its defence (or deletes it first). -- Steelpillow 18:50, 22 May 2007 (UTC)
Another quote:
Is this name "edge figure", correct? Can anybody provide a reference? It's important not to delete this un-referenced material without checking, because the (2D) dual of this figure is a face of the dual polychoron or honeycomb (e.g. by Dorman Luke's construction). But has it got the correct heading? -- Steelpillow 19:06, 22 May 2007 (UTC)
I think for purposes of this article a solid picture illustrates the concept better than a Schlegel diagram. — Tamfang ( talk) 18:27, 25 December 2008 (UTC)
I'm not sure that edge figures are adequately represented in reliable sources. In particular Dr. Klitzing does not appear to have sufficient record of peer-reviewed publications for his web site to be an authoritative source. The fact that a few of us talk about them informally is also not sufficient. As one illustration of the reasons behind this attitude consider that the vertex figure of a higher-dimensional edge figure is not so much to do with an edge as with an (n-2)-cell; in this context the term "edge figure" is inappropriate and its usage immature. I should like to see either a clear path towards adequate referencing, or deletion of this section. — Cheers, Steelpillow ( Talk) 18:46, 24 May 2011 (UTC)
What is single-ringed? At least, where I may read about it? Is it about mirrors in Coxeter diagrams? Jumpow ( talk) 12:37, 3 November 2015 (UTC)
Also not fully clear next sentence:
Edges in second case means figure type? Jumpow ( talk) 14:34, 3 November 2015 (UTC)
The comment(s) below were originally left at Talk:Vertex figure/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
This page needs a lot of work - to add a lot of important elementary information, and to tidy-up and expand the more advanced stuff already here. -- Steelpillow 18:52, 22 May 2007 (UTC) |
Last edited at 18:52, 22 May 2007 (UTC). Substituted at 20:19, 1 May 2016 (UTC)
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Is Richard Klitzing's web site a WP:RS for the "edge figure"? The article currently cites the page at http://www.bendwavy.org/klitzing/explain/verf.htm — Cheers, Steelpillow ( Talk) 18:14, 17 March 2018 (UTC)
Currently this article does not contain a single image of a polyhedron to illustrate its vertex figure. I tried to change this by including three images of Archimedean solids and their duals, including the one on the right. This was reverted by Steelpillow. I think dual compounds are a good example, and cutting in the middle of edges is one of the methods described in the article. Any better ideas? Watchduck ( quack) 18:38, 17 March 2018 (UTC)
It would be interesting to hear your opinion on how the vertex figures of Archimedean solids should be illustrated in their respective articles: Talk:Archimedean solid#Images Greetings, Watchduck ( quack) 02:03, 16 April 2018 (UTC)
@ Watchduck: You are cherry-picking snippets to try and back your case. The text in TSOT accompanying the illustrations on p.289 states categorically that "the vertex figure of the cuboctahedron (Figure 21.1 left) and icosidodecahedron are rectangles whose sides are numbered ...". The drawing shows a slice through a polyhedron, the "pyramid" is merely that part to one side of the slice, with the overall polyhedral form remaining intact. It does not, as you claim, merely "show a pyramid cut from the solid". Note the close correspondence between Fig 21.1 and the cuboctahedron drawing I mentioned above.
I am not sure if polychora have been mentioned here, but if a pyramid does occur as a vertex figure then it is of some four-dimensional polychoron. It is, as I have said, mathematical madness to use the same pyramid in an attempt to illustrate the lower-dimensional vertex figure of a polyhedron. The central point adds nothing to the description here, save confusion.
— Cheers, Steelpillow ( Talk) 17:06, 27 July 2018 (UTC)
This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||||||||||||||||||||
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I made a vertex figure symmary chart on a talk subpage for reference:
Having just added a picture and some explanation, it occurs to me that it is also relevant to dual polyhedra. Should it:
-- Steelpillow 20:15, 3 June 2007 (UTC)
To quote a current snippet:
What is "imaginary" supposed to mean in this context? Perhaps "skew" is meant. And what does the construction described have to do with vertex figures? It seems quite trivial and has no real theoretical or practical significance that I am aware of. I think this should not be here, and I will delete it in a few days if nobody comes to its defence (or deletes it first). -- Steelpillow 18:50, 22 May 2007 (UTC)
Another quote:
Is this name "edge figure", correct? Can anybody provide a reference? It's important not to delete this un-referenced material without checking, because the (2D) dual of this figure is a face of the dual polychoron or honeycomb (e.g. by Dorman Luke's construction). But has it got the correct heading? -- Steelpillow 19:06, 22 May 2007 (UTC)
I think for purposes of this article a solid picture illustrates the concept better than a Schlegel diagram. — Tamfang ( talk) 18:27, 25 December 2008 (UTC)
I'm not sure that edge figures are adequately represented in reliable sources. In particular Dr. Klitzing does not appear to have sufficient record of peer-reviewed publications for his web site to be an authoritative source. The fact that a few of us talk about them informally is also not sufficient. As one illustration of the reasons behind this attitude consider that the vertex figure of a higher-dimensional edge figure is not so much to do with an edge as with an (n-2)-cell; in this context the term "edge figure" is inappropriate and its usage immature. I should like to see either a clear path towards adequate referencing, or deletion of this section. — Cheers, Steelpillow ( Talk) 18:46, 24 May 2011 (UTC)
What is single-ringed? At least, where I may read about it? Is it about mirrors in Coxeter diagrams? Jumpow ( talk) 12:37, 3 November 2015 (UTC)
Also not fully clear next sentence:
Edges in second case means figure type? Jumpow ( talk) 14:34, 3 November 2015 (UTC)
The comment(s) below were originally left at Talk:Vertex figure/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
This page needs a lot of work - to add a lot of important elementary information, and to tidy-up and expand the more advanced stuff already here. -- Steelpillow 18:52, 22 May 2007 (UTC) |
Last edited at 18:52, 22 May 2007 (UTC). Substituted at 20:19, 1 May 2016 (UTC)
Hello fellow Wikipedians,
I have just modified one external link on Vertex figure. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
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Cheers.— InternetArchiveBot ( Report bug) 21:22, 20 July 2016 (UTC)
Is Richard Klitzing's web site a WP:RS for the "edge figure"? The article currently cites the page at http://www.bendwavy.org/klitzing/explain/verf.htm — Cheers, Steelpillow ( Talk) 18:14, 17 March 2018 (UTC)
Currently this article does not contain a single image of a polyhedron to illustrate its vertex figure. I tried to change this by including three images of Archimedean solids and their duals, including the one on the right. This was reverted by Steelpillow. I think dual compounds are a good example, and cutting in the middle of edges is one of the methods described in the article. Any better ideas? Watchduck ( quack) 18:38, 17 March 2018 (UTC)
It would be interesting to hear your opinion on how the vertex figures of Archimedean solids should be illustrated in their respective articles: Talk:Archimedean solid#Images Greetings, Watchduck ( quack) 02:03, 16 April 2018 (UTC)
@ Watchduck: You are cherry-picking snippets to try and back your case. The text in TSOT accompanying the illustrations on p.289 states categorically that "the vertex figure of the cuboctahedron (Figure 21.1 left) and icosidodecahedron are rectangles whose sides are numbered ...". The drawing shows a slice through a polyhedron, the "pyramid" is merely that part to one side of the slice, with the overall polyhedral form remaining intact. It does not, as you claim, merely "show a pyramid cut from the solid". Note the close correspondence between Fig 21.1 and the cuboctahedron drawing I mentioned above.
I am not sure if polychora have been mentioned here, but if a pyramid does occur as a vertex figure then it is of some four-dimensional polychoron. It is, as I have said, mathematical madness to use the same pyramid in an attempt to illustrate the lower-dimensional vertex figure of a polyhedron. The central point adds nothing to the description here, save confusion.
— Cheers, Steelpillow ( Talk) 17:06, 27 July 2018 (UTC)