Talk:Face (geometry)

The Formal Definition here really SUCKS, and without references it is hard to evaluate for cleanup. spacetime??? intersection of any supporting hyperplane of P and P? Nonsense and errors for all I know! Tom Ruen 06:50, 14 October 2006 (UTC)[reply]

I am trying to understand this definition so I can help my child do his homework. Nowhere does it say whether a face is flat, or planar. Please write something that I can understand. Thank you.

68.6.69.34 03:37, 23 February 2007 (UTC)[reply]

this does not make a dot of sense —Preceding unsigned comment added by 79.64.78.217 (talk) 17:07, 12 September 2007 (UTC)[reply]

Holes

Can a surface still be a face if it has a hole in it? 24.85.161.72 (talk) 21:02, 27 March 2013 (UTC)[reply]

A good question, doesn't seem covered here. There are other special cases of general polygons that cause problems - nonplanarity, concavity, self-intersection, and self-contacted boundaries. In all cases triangulation (geometry) would seem to offer an workable solution. That is, if you take a polyhedron and triangulate its faces with new edges that represent the hole, then you can work from those simple polygon faces. Afterwards, you could consider the collection of triangles glued together back and consider what restrictions you want to allow. Tom Ruen (talk) 22:54, 27 March 2013 (UTC)[reply]

Face, n-face, and Facet?

There is discussion on these three confusing usages of face at: Template_talk:Infobox_polychoron#Face. I think this article is the problem. Tom Ruen (talk) 05:57, 19 May 2013 (UTC)[reply]

The formal part of the article looks to be completely in agreement with standard research usage to me. However, the lead section somewhat contradicts it. The problem, as I see it, is that some of our articles (and the template in question) use "face" in a way that does not match the formal definition here, to mean only the 2-faces. It is the other articles (and the lead of this article) that need to be corrected. —David Eppstein (talk) 06:30, 19 May 2013 (UTC)[reply]

ETA: I've edited the article to fix some technical mistakes (the formal definition needs to intersect the polytope with a halfspace, not a hyperplane) and to remove some strange notions about space-time. I also rewrote the lead to more accurately reflect the contradiction between different meanings. I also added some much higher quality sources than the links previously included with the article (which are still present as they were before in the external links section). —David Eppstein (talk) 06:43, 19 May 2013 (UTC)[reply]