Talk:Density (polytope)

Polygon density - Applicability

 * Copy-pasted from Talk:Polygon density, following merging of content &mdash; Cheers, Steelpillow (Talk) 21:19, 7 January 2012 (UTC)

I am removing the text: "The interior area of a polygon can be colored by a constant density within each region. Peter Cromwell calls these regions layers" and hacking at related material, because this is wrong. Cromwell's "layers" refer to the boundary rather than to regions. Cromwell only discusses density in the context of the whole figure - see density (polytope) for the more general picture. Yes, many of us today do talk of the density of individual regions, but I know of no reputable reference for this usage, so AFAIK it constitutes original research. If you know of a good reference, please fix my edit! -- Cheers, Steelpillow (Talk) 18:32, 29 November 2009 (UTC)

Polygon density - proposed merge & rename
This article and the one on polygon density are both stubs and there is little chance of meaningful expansion. Polyhedron density redirects here. Polygon density is merely the two-dimensional case of polytope density, so I propose we merge it into here. &mdash; Cheers, Steelpillow (Talk) 12:19, 30 December 2011 (UTC)

Also, since I find the current article title to be awkward, how about renaming it – effectively merging both articles into a new one – as either Density (polytope) or Density of a polytope, whichever is the more formally correct for this encyclopedia. &mdash; Cheers, Steelpillow (Talk) 12:27, 30 December 2011 (UTC)


 * I have no problem, and in fact, might equally be merged into Regular_polytope (or somewhere near that) since it only appears to be used in relation to the regular star polytopes (as well, there's none above 4D!). Tom Ruen (talk) 04:13, 31 December 2011 (UTC)
 * Okay, backtrack! Coxeter did name densities of the uniform polyhedra (1954 paper), at least the non-hemi ones. Tom Ruen (talk) 04:29, 31 December 2011 (UTC)


 * Support merge – polygon density can’t be meaningfully expanded, and really falls as a case of this.
 * Regarding title, Density (polytope) seems best.
 * Regarding content, this does seem a distinct concept of independent interest, though not esp. long. A table of the density of the regular 3D and 4D star polytopes (and uniform polyhedra) may be interesting (tables already exist at the articles, but a stripped down one here might be nice).
 * Thanks!
 * —Nils von Barth (nbarth) (talk) 04:54, 1 January 2012 (UTC)

Consolidation now done. Stuff on uniform figures and table of densities to come. &mdash; Cheers, Steelpillow (Talk) 16:38, 2 January 2012 (UTC)

Why the revert?
Why were the Polygon density and polytope density redirects deleted? Secondly, Guy, if you wanted to add densities from Coxeter's paper to the uniform star polyhedron articles, it can be added to the database file Template:Uniform_polyhedra_db as a new data-field (polyhedron entries classed by their BSA, but other indices available ) and then add a density entry in the table template Template:Uniform_polyhedron_stat_table. Thirdly, I'd assume the duals to the uniform stars have the same density? Tom Ruen (talk) 21:16, 2 January 2012 (UTC)
 * Looks like it was moved back to polytope density. I also made Polygon density and Polyhedron density as redirects, and anchored to specific sections in this article. Tom Ruen (talk) 19:04, 3 January 2012 (UTC)


 * Tom, I have no idea why the move got reverted. Ankit Maity dropped me a note about how I should have used a different mechanism to make the change. Next thing is, it gets undone. I'll drop 'em a line and invite an explanation. Will follow up your points about the database once we have a stable page name to work on. &mdash; Cheers, Steelpillow (Talk) 21:38, 3 January 2012 (UTC)
 * It's because the article is not about the density's polytope but it's about polytope's density. Cheers.-- Ankit Maity  Talk •  contribs 06:23, 4 January 2012 (UTC)
 * But there are many examples of this usage, it is quite standard. For example Line (geometry) is about the use and study of lines in the theory of geometry as opposed to other usages of the line, and not about the application of geometry to a given line. Similarly, this article is about the use and study of density in the theory of polytopes, hence Density (polytope) is appropriate. You appear to have it the wrong way round. &mdash; Cheers, Steelpillow (Talk) 22:21, 4 January 2012 (UTC)

Certainly copy-and-pasted moves should not be done, since they destroy the article's edit history. According to the current history, this article was called "Density (polytope)", then it was moved to "Polytope density", then to "Density (Polytope)" (with an incorrectly capitalized initial "P"), then finally back to "Density (polytope)". I did that last move a few minutes ago. That required me to delete the redirect page that had been created by the earlier move from "Density (polytope)" to "Polytope density". I then restored the edit history, so the history of the deleted redirect page should appear. Michael Hardy (talk) 03:06, 7 January 2012 (UTC)
 * And before that I temporarily merged "Polygon density" into "Polytope density" prior to creating "Density (polytope)" to hold the merged content. Anyway, thanks for sorting it out. Just now I moved here the content of Talk:Polygon density, which I forgot to do earlier. &mdash; Cheers, Steelpillow (Talk) 21:30, 7 January 2012 (UTC)
 * If that's what in other article's case, then it's reallllllllllly the wrong way. I apologize. It's like drunk men walking straight. (Brit speaking style.) Am still a li'l rookie? (Amer speaking style. Ain't I got it right.) -- Ankit Maity  Talk •  contribs 12:57, 8 January 2012 (UTC)
 * The logic of the brackets is that the page is about Density (but of a polytope specifically, not just any kind). We use it for quite a few mathematics pages. HTH &mdash; Cheers, Steelpillow (Talk) 14:19, 8 January 2012 (UTC)

Requested move

 * The following discussion is an archived discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section. 

The result of the move request was: moved by. (non-admin closure) Jenks24 (talk) 06:05, 9 January 2012 (UTC)

Density (Polytope) → Density (polytope) – Primary reason for requesting this move is that I mistakenly capitalised "polytope" when attempting to make the move agreed above. The controversial bit is that another user (see also above) disputes the title for reasons which I have argued to be spurious. I asked both here and on their user page for clarification but the user has not responded, despite making edits elsewhere over the last couple of days. Hoping I have waited long enough for the requested move to go ahead - apologies if I still haven't got the etiquette right yet, I am trying (honest). &mdash; Cheers, Steelpillow (Talk) 19:47, 6 January 2012 (UTC)
 * The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.

Hemipolyhedra
I just commented out the claim that "[for a hemipolyhedron] the center may be counted as half a point, or more precisely one may define the density as half the number of facet crossings of a line from infinity, through the center, passing out the other side to infinity." This claim is unreferenced and, I believe, unsustainable. For example the tetrahemihexahedron cannot sensibly be given a density of 1 1/2. I left it in the page code for the time being, just in case someone can reference it. &mdash; Cheers, Steelpillow (Talk) 14:56, 7 January 2012 (UTC)