Talk:Star polygon
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The introduction says that "star" polygons are by definition regular, which surprises me. Is there really such a convention? What would you call the figure formed by the diagonals of an irregular (but convex) pentagon? —Tamfang 06:36, 23 March 2006 (UTC)
- I was surprised also. It implies "star"="regular nonconvex", so anything else is merely "nonconvex" or "complex". I don't have an explanation for the definition limitation. Tom Ruen 09:36, 23 March 2006 (UTC)
- I was also surprised, but I checked another reference and it also does say they are regular. of course, since most of the interesting properties are numeric rather than geometric, it doesn't actually matter. -- Securiger 08:52, 28 August 2006 (UTC)
I removed this, doesn't belong in generalized article on geometry - please move to pentagram if anyone wants to keep it! Tom Ruen 03:28, 27 September 2006 (UTC)
- It has been stated that creating a five-pointed star in a similar fashion was one of the esoteric teachings of the Pythagoreans. Divulging that secret was punishable by death.[citation needed]
This article is a bit of a mess. I rearranged a bit, but needs more work.
Also there's also two distinct definitions of star polygon used in Branko Grunbaum's book Tilings and Patterns (Chapter 2, section 5), the other meaning from Kepler, which actually considers concave simple 2n-gons as the outlines of a complex connected n-gon (shown here), and used in tilings. Grunbaum uses notation |m/n| for these concave form. He also uses {nα}, for an n-sided star with vertex internal angle α<180*(1-2/n). Anyway, thought I'd throw this out here in talk at least, while not prepared to add anything for now. Tom Ruen 03:38, 27 September 2006 (UTC)
