Talk:Complex polygon
From Wikipedia, the free encyclopedia
[edit] Complex polygons?
Comment below moved from Talk:Kepler-Poinsot_solid
- Where does the term complex polygon come from? I have done a fair bit of geometry, and the only 'complex polygons' I have come across are those where the polygonal boundary is in several separate parts, creating holes in the figure. I have never seen it used to describe selfintersecting polygons. Please either give a reference to this usage or change the wording. Steelpillow 22:34, 21 December 2006 (UTC)
-
-
- D'oh! Silly me! Of course there is another, and more important, kind of complex polygon: a polygon in the complex plane. See for example Coxeter's 'Regular Complex Polytopes', Cambride University Press, 1974.
-
-
-
- There are hints in that book of an earlier definition, where the polygon has more that two vertices on a given side, or more than two sides connecting at a vertex, in the real plane.
-
-
-
- The only references I know of to the definition I gave first, of multiple closed boundaries to make holes, are on the web. H'mm. Tom, you and I had better ask around. We may not get many answers until after Christmas, I guess...
-
-
-
- I suppose we'll need a page on Complex polytope, link from the Polytope page, etc. BTW, the Polytope and Star polygon pages also have the same mistaken use of 'complex' polygon. We need to check for more.
-
-
-
- With respect to selfintersecting figures, Branko Grünbaum has in the past called them 'coptic' (convex and midly dimpled figures are 'acoptic') but it doesn't seem to have caught on. Steelpillow 19:57, 22 December 2006 (UTC)
-
- I had wondered about Coxeter's book Regular Complex Polytopes, what complex meant. The old book is a bit pricy online. I guess there's two editinos, 1974 [1], and 1991 2nd [2]. If you have a copy, adding Complex polytope article would be good! Tom Ruen 22:03, 22 December 2006 (UTC)
[edit] Recent tidy-up
Tom, I just corrected some factual errors which crept into your tidy-up, added something I'd forgotten, and did a bit more tidying to help clarify it all. Hope all is now sensible. Steelpillow 11:16, 26 December 2006 (UTC)
