Talk:Dual polyhedron

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Mathematics rating:	Start Class	Mid Priority	Field: Geometry
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. Would benefit from: a diagram showing polar reciprocity, a full section on Wenninger's 'infinite prism' duals, perhaps a table of some common or interesting dual pairs (e.g. the regular pairs and the Csaszar and Szilassi polyhedra).

The statement "If a polyhedron has an element passing through the center of the sphere, it will have an infinite dual." makes no sense, since it there is no definition (or even explanation) what "an infinite dual" means. No definition of "polyhedron" admits vertices or edges or faces "at infinity.

[edit] Generalize to dual polytopes?

Many of the concepts described in this article also apply to n-dimensional polytopes. Would it make sense to extend this article so that it applies to both? There are quite a good number of articles on 4-dimensional polytopes (see polychora and uniform polychora), which would make good use of a more general description of duals.—Tetracube 22:14, 17 February 2006 (UTC)

Good to add something! Choices?

1. Rename to Dual polytope and expand with divided sections by dimension? (starting with regular polygons as self-duals)
2. Create Dual polychoron article and move/expand the 4D/honeycomb content there?
3. Keep Dual polyhedron, add Dual polychoron, and add Dual polytope with dimensional article references?

Tom Ruen 23:10, 17 February 2006 (UTC)

I prefer to put them together, since otherwise there will be a lot of needless repetition. So option 1 sounds good to me.—Tetracube 01:54, 18 February 2006 (UTC)

Sounds good! I wonder who else is watching?

Incidentally, there's LOTS of links to this article. I've found it useful elsewhere to link expanded by article/headers. In this case like dual polyhedron and dual tiling and dual polychora and dual honeycomb for dimensional subsections. That works well as long as headers are not changed! Tom Ruen 04:08, 18 February 2006 (UTC)

As these articles pad out, I think this begins to make for rather large pages. For example, consider listing all the interesting dual pairs in every dimensionality all on a single page! <shudder!>.

I'd like to keep this page fairly simple, and add a Dual polytope page for the general theory, e.g. to do justice to the duality of abstract polytopes. Dual polychora? well, I'd keep it as part of Dual polytopes until it all gets too big, then float it off on its own. -- Steelpillow 21:26, 4 June 2007 (UTC)

[edit] Consensus to rename to Dual polytope?

YES

1. Tom Ruen 02:43, 18 February 2006 (UTC)
2. Dshin 19:39, 23 March 2006 (UTC)

NO

1. Steelpillow 21:26, 4 June 2007 (UTC)