Talk:Star polygon

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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. Hmm... the lead is weak but the rest of the article is B class. fix it and then self promote.--Cronholm144 00:36, 21 May 2007 (UTC)

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 {n_α}, 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)

Is a star actually able to be considered a geometric shape? Stars vary in the amount of vertices and sides. All geometric shapes, when defined as whatever shape, is mentioned to have this many sides and this many points. To have less points or less sides classifies it as a different shape (if physically possible). Ulgar 19:21, 30 July 2007 (UTC)

Sorry, I don't understand your question. Tom Ruen 19:32, 30 July 2007 (UTC)

The term "star" defines a class of geometric shapes, in the same way that a term like "polygon" or "configuration" does. Some classes of shape are defined according to some number, such as the class of pentagons, but other classes are not. And some classes overlap, such as stars and pentagons. An individual shape may then be described specifically, such as a "regular star pentagon" or "Reye's configuration." Hope this helps. -- Steelpillow 20:13, 30 July 2007 (UTC)

Ah, thank you, Steelpillow. In all honesty, a friend and I were arguing about whether stars could be considered a shape like square and pentagon and rhombus. The definition of a star was one of where a person goes from the point of one to another blah blah blah... it wasn't as the other shapes. However, putting it into that shapes are actually just different categories of which all polygons can fall under, I see now how the category "star" can exist, because its defining sets of rules differ from other typical categories like square and pentagon and rhombus. Now that I think of it, I should have paid more attention to that different shapes can have the same number of sides and vertices but MORE qualifiers like angle. I guess I lose the argument. :P Ulgar 01:45, 1 August 2007 (UTC)

[edit] Merge with star polyhedron?

I don't support a merge - it's like saying merge polygon and polyhedron. The other article is short and needs expanding, but this one also can use expanding as well - including Kepler's definition of stars for tilings. Tom Ruen 17:42, 3 August 2007 (UTC)

It is also worth comparing with stellation, which IS a multidimensional article now. Stellations and polytopes are closely related in appearance, but also categorically different constructions and topology. Tom Ruen 17:45, 3 August 2007 (UTC)

Merging is quite wrong. I'm removing the suggestion -- Steelpillow 07:47, 4 August 2007 (UTC)