Wikipedia talk:WikiProject Polyhedra

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Two points

@Dedhert.Jr,

1. Do you still need help with the table?
2. Do you mind if I archive the old posts on this talk page? Since it's starting anew, and all.

Cheers! — Remsense诉 03:25, 20 January 2024 (UTC)

@Remsense Yes, please. Archiving old posts does not really matter for me. Dedhert.Jr (talk) 03:53, 20 January 2024 (UTC)

Dedhert.Jr, I appear to have fixed it—you can now see the totals on the ends. All articles so far lack importance ratings though, so there are all zeroes the body of the matrix itself. — Remsense诉 05:47, 21 January 2024 (UTC)

Thank you. I just need to create more categories on each red links. Dedhert.Jr (talk) 05:57, 21 January 2024 (UTC)

Dedhert.Jr, how do you feel about the scope of the project being all polytopes? i think it's fine for the project name itself to be off, but I worry about the category names in kind. — Remsense诉 09:27, 21 January 2024 (UTC)

@Remsense We do have already the WikiProject, a so-called, WikiProject Uniform Polytopes. Honestly. I have no idea about this one project, but if you want to make them active again, it's fine. I do not particularly care about it. Dedhert.Jr (talk) 12:32, 21 January 2024 (UTC)

That wikiproject is not active in the past decade, and should probably be archived/deleted. Treating "wikiproject polyhedra" to include any polytopes (uniform or otherwise) seems entirely reasonable. The project could plausibly also be widened to also include tilings, crystallographic groups, etc. –jacobolus (t) 01:57, 22 January 2024 (UTC)

@Remsense By the way in special:diff/1197603420 you added a duplicate template to talk:isosceles triangle. (I reverted it.) –jacobolus (t) 06:04, 21 January 2024 (UTC)

Unassessed Polyhedra articles

Please note that Category:Unassessed Polyhedra articles is a redlinked category with two pages in it, on both of which it's a template-generated category that can't be removed. If you want your WikiProject template to be generating categories, then it's your project's responsibility to be on top of bluing in all redlinked categories immediately, and not leave them lingering for the categorization project to have to clean up later — so if this project wants that category to exist, then please create it yourselves right away, and if you don't, then edit the template so it doesn't generate it at all. Thanks. Bearcat (talk) 04:13, 23 January 2024 (UTC)

@Bearcat Sorry for late response and thank you. Will try to implement your suggestion. Dedhert.Jr (talk) 12:44, 25 January 2024 (UTC)

polyhedral graphs and graphic polyhedra

I wonder how hard it would be to illustrate each article on a polyhedral graph with a rotating image of the corresponding canonical polyhedron. —Tamfang (talk) 05:45, 5 February 2024 (UTC)

Not an expert in graph theory, but I will ping @David Eppstein for the answer (my apologies). Dedhert.Jr (talk) 06:04, 5 February 2024 (UTC)

Constructing the canonical polyhedron involves constructing a circle packing on a sphere and then Möbius-transforming the packing into a position where the centroid of the points of tangency is the center of the sphere. I have implemented the circle packing part but I don't know about implementations of the second part. I suspect it would work to simply iteratedly apply transformations that take the current centroid to the center (and don't spin, and maybe damp them a little), and if so then an implementation would be conceptually straightforward at least, but I don't know a reference for a proof offhand.

When I needed a canonical square pyramid for a recent blog post (https://11011110.github.io/blog/2023/11/20/some-pyramidology.html) I couldn't find a reference and resorted to using hand calculation to work out its exact dimensions, but that only worked because it was so simple. —David Eppstein (talk) 06:17, 5 February 2024 (UTC)

This seems like it should be quite a straightforward (more or less) 1-dimensional optimization problem, which should be numerically solvable with something analogous to the secant method (or any other standard root-finding or optimization method), if nothing fancier is available. How do we get a starting circle configuration? (Aside: is there a particular reason to want the centroid of the points to line up with the center of the sphere, beyond just picking some criterion guaranteeing a unique answer? It seems like a slightly arbitrary choice.) –jacobolus (t) 08:09, 5 February 2024 (UTC)

There's relevant discussion at https://math.stackexchange.com/questions/3272196/computing-canonical-polyhedra-without-numerical-methods and https://student.cs.uwaterloo.ca/~cs763/Projects/tiffany.pdf –jacobolus (t) 00:34, 6 February 2024 (UTC)

(Tangential aside: @David Eppstein do you know if anyone ever tried to turn an Apollonian gasket into a "canonical shape" by this method? Seems like a funny idea.) –jacobolus (t) 02:59, 6 February 2024 (UTC)

All Apollonian gaskets are the same under Möbius transformation. A canonical construction for a set of only one thing isn't usually very useful. The canonical one is presumably the one with three equal-sized circles tangent to each other and to the outer circle. —David Eppstein (talk) 05:50, 6 February 2024 (UTC)

Oh good point, and fair enough (the canonical one is probably going to have 4 identical circles on the sphere). I wonder if anyone tried plotting that convex shape; you start with a tetrahedron and then shave various bits off the corners. –jacobolus (t) 07:35, 6 February 2024 (UTC)

Old task and some new featuring similarity main article of WP:WPM

I do think there are things to be changed in this project. Should the old tasks would be replaced, and focused on what lies ahead now? Also, the main article is too much bunch of lists, and probably need to clean up; is it possible to feature the similar things like WP:WPM? Dedhert.Jr (talk) 15:40, 28 February 2024 (UTC)