Template talk:Infobox 4-polytope

Documentation

This template needs some documentation. Kaldari (talk) 04:45, 18 December 2010 (UTC)

Surely. It was intended for all the uniform polychora, but currently only tested on regular forms by Special:WhatLinksHere/Template:Infobox_polychoron. Tom Ruen (talk) 04:52, 18 December 2010 (UTC)

Symmetry group

Note: Symmetry group and Coxeter group are largely the same thing, at least for pure reflectional symmetry. (snub 24-cell and grand antiprism are exceptions with rotational symmetry, but I've not seen a full enumeration of variations) Tom Ruen (talk) 05:36, 18 December 2010 (UTC)

Hmm, I was wondering about that. Is it useful to have both available for use in the infobox, or should it be standardized on one or the other. Kaldari (talk) 05:38, 18 December 2010 (UTC)

For example, does 57-cell have a Coxeter group, or would it need to use the Symmetry group parameter instead? Kaldari (talk) 05:41, 18 December 2010 (UTC)

I don't know much of the possible symmetries of the abstract polytopes, not even regular ones. We could put coxeter groups under a label symmetry group, but the question is what should that link to (the current link is too general). There's no clear (summary) wiki info on listing higher symmetry groups (above 3D) except Coxeter groups. Perhaps there should be parallel templates, and this one renamed Infobox uniform polychoron? Tom Ruen (talk) 05:47, 18 December 2010 (UTC)

Face

Who decided that the 2-faces should be called faces? In research-level mathematics on polytopes, that's not what "face" means: The empty set, vertices, edges, cells, and the polytope itself are also all faces; see e.g. face lattice. Instead of 2-faces, it would be correct to call them ridges. Polygons would also work. —David Eppstein (talk) 04:52, 19 May 2013 (UTC)

True, but is there a problem? They are called faces in polyhedra. Calling them polygons isn't right either, since they are elements. We can differentiate between n-cube and cube, but a cube is still a cube. Facet/Ridge/Peak terminology exists for (n-1),(n-2), and (n-3) dimensional polytope elements, but that's in the context of n-polytope usage rather than a specific n. Cell (geometry) can equally be called 3-face, and hypercell is a bad compromise for 4-face. Tom Ruen (talk) 05:32, 19 May 2013 (UTC)

The problem is that I want to be able to add information to articles like octahedral prism that "it has 81 nonempty faces, the minimum possible for a symmetric 4-polytope (see Kalai's 3^d conjecture)". But because "face" is used prominently in the article to mean the wrong thing it's not possible to do that. There are other ways we can say 2-face but there are not other ways that we can say the other thing. And promoting "face" to mean the wrong thing may also contribute to bad edits such as this one (by someone thinking faces and facets are synonyms) that I just undid.—David Eppstein (talk) 05:40, 19 May 2013 (UTC)

Sorry, not sure I follow, but maybe 2-face being linked to what is more an n-face article is the confusing point? In which case I agree (clarification is needed THERE!) I mean there really are 3 competing definitions: face=2-face, face=k-face, and facet=(n-1)-face for n-polytope! Tom Ruen (talk) 05:55, 19 May 2013 (UTC)

I added a section at Talk:Face_(geometry) where we can get more input. Tom Ruen (talk) 05:58, 19 May 2013 (UTC)

If we called the two-dimensional faces "polygons" rather than faces in this template, it would be completely unambiguous. Lack of ambiguity is a good thing in mathematics, no? —David Eppstein (talk) 06:32, 19 May 2013 (UTC)

I gave my initial thoughts at Talk:Face_(geometry). — Cheers, Steelpillow (Talk) 12:46, 19 May 2013 (UTC)

Volume?

Is there any reason that Volume shouldn't be added as a parameter?Naraht (talk) 03:43, 2 March 2020 (UTC)