Definition talk:Adjacent Faces

I don't think we want this to be a redirect&mdash;faces can be adjacent whether or not the graph is planar. Some more structure is needed, of course, but this whole concept arises originally from solid geometry, not graph theory. --Dfeuer (talk) 22:01, 29 May 2013 (UTC)


 * Faces are defined only for planar graphs. Thought you said you didn't know anything about graph theory. --prime mover (talk) 22:04, 29 May 2013 (UTC)


 * I should have been clearer. Graphs aren't inherently involved. For example, a triangulation of a torus won't form a planar graph, but it's perfectly sensible to speak of adjacent faces of it. --Dfeuer (talk) 22:17, 29 May 2013 (UTC)


 * I should have been more emphatic. On this site, faces are defined only for planar graphs. Until such time as a viable definition can be crafted for what a face is on a non-planar graph, there is no point in trying to extend the concept of adjacency to a definition of a face which is on such a non-planar graph.


 * In short we're back to the old problem of adding random "wisdom" from random googling of random (and in many cases useless and dangerously misleading) websites without having established the context into which these definitions arise. --prime mover (talk) 05:17, 30 May 2013 (UTC)


 * Let me say more emphatically: I am not talking about graph theory. I am talking about geometry. Faces, edges, and vertices are not just graph theory concepts. --Dfeuer (talk) 06:25, 30 May 2013 (UTC)

Let me put the definitive call. Until there is a background in geometry that allows us to define faces of the boundary of some volume in 3D (or perhaps even higher dimensions; this isn't my forte) a redirect is fine.

Oh, and as administrators, lead by example already. It's tiresome to observe that your quibbles haven't diminished over the course of months, even after I have repeatedly pleaded for this. I'm not interested in arguments; you've had your opportunity to blame one another, I don't want to hear it. Just lead by example. &mdash; Lord_Farin (talk) 08:59, 30 May 2013 (UTC)