Talk:Star polygon

message: 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)
replies: text: 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)
replies: text: 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)

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

text: 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)
replies: text: 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)

text: That'd be me (my username is Popisfizzy). I changed it because when I think "star", I tend to think moreso of the spherical cellestial objects makes of plasma, and not the geometric shape. I suppose I shouldn't've been so hasty. 207.255.35.246 (talk) 05:39, 21 January 2009 (UTC)

text: "A star polygon is a non-convex polygon which looks in some way like a star. Only the regular ones have been formally defined and studied in any depth; star polygons in general have never been formally defined. They are not the same thing as polygons which are star domains."
I also retrieved the difficulty over compound stars and Schläfli symbols. This is a deep one - its origin goes back to Poinsot, and the modern usage has only recently become established (or maybe it hasn't yet and we need to discuss both usages?).
-- Cheers, Steelpillow (Talk) 11:39, 18 January 2009 (UTC)

text: Well, you know, any stellated polygon consists of diagonals of its convex hull.  Any convex polygon (>4) has diagonals that can make a star, but not every such polygon can be stellated, because of parallel edges.  —Tamfang (talk) 17:50, 18 January 2009 (UTC)

text: Good point about the convex hull.  On the other hand, if I say definition X is not general enough to cover condition Y it's no refutation to point out that it does cover condition Z – unless you're proposing to confine the discussion to the projective plane! —Tamfang (talk) 03:39, 19 January 2009 (UTC)

text: The idea of local convexity does in fact include bow-ties, because each vertex (the "local" one) is considered in isolation. But sadly all that is unpublished OR and we cannot include it. -- Cheers, Steelpillow (Talk) 20:08, 31 January 2009 (UTC)
thread_title: definition of "star" polygons

message: Two contributors have recently made changes to the lead definition. Also, Tamfang has edited the discussion of regular compounds. I do not agree fully with these changes, so I have reverted them in the hope that we can reach agreement here before making further changes.
An anonymous visitor talked about the "artistic depiction of a star". I do not think I am the only one dissatisfied with this - there is no aesthetic or cultural judgement, and hence no "art" in the mathematical concept: it is a pragmatic description.
:That'd be me (my username is Popisfizzy). I changed it because when I think "star", I tend to think moreso of the spherical cellestial objects makes of plasma, and not the geometric shape. I suppose I shouldn't've been so hasty. 207.255.35.246 (talk) 05:39, 21 January 2009 (UTC)
replies: text: "A star polygon is a non-convex polygon which looks in some way like a star. Only the regular ones have been formally defined and studied in any depth; star polygons in general have never been formally defined. They are not the same thing as polygons which are star domains."
I also retrieved the difficulty over compound stars and Schläfli symbols. This is a deep one - its origin goes back to Poinsot, and the modern usage has only recently become established (or maybe it hasn't yet and we need to discuss both usages?).
-- Cheers, Steelpillow (Talk) 11:39, 18 January 2009 (UTC)

text: Well, you know, any stellated polygon consists of diagonals of its convex hull.  Any convex polygon (>4) has diagonals that can make a star, but not every such polygon can be stellated, because of parallel edges.  —Tamfang (talk) 17:50, 18 January 2009 (UTC)

text: Good point about the convex hull.  On the other hand, if I say definition X is not general enough to cover condition Y it's no refutation to point out that it does cover condition Z – unless you're proposing to confine the discussion to the projective plane! —Tamfang (talk) 03:39, 19 January 2009 (UTC)

text: The idea of local convexity does in fact include bow-ties, because each vertex (the "local" one) is considered in isolation. But sadly all that is unpublished OR and we cannot include it. -- Cheers, Steelpillow (Talk) 20:08, 31 January 2009 (UTC)
thread_title: Definition revisited

message: 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)
replies: text: 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)
replies: text: Merging is quite wrong. I'm removing the suggestion -- Steelpillow 07:47, 4 August 2007 (UTC)
thread_title:  Merge with [[star polyhedron]]? 

message: The search was for "star polygon*" (with wildcard after "polygon"), and the results are sorted by date.
--Jtir (talk) 11:03, 2 August 2008 (UTC)
thread_title:  Literature search results from the ArticleFirst datebase 

message: Uniform polyhedron vertex figures: (White lines)
:
:
:
:
: Many more at List of uniform polyhedra
:Tom Ruen (talk) 00:02, 4 August 2008 (UTC)
thread_title:  Quadrilateral (bow-tie) examples 

message: User:Taxman recently changed the lead, and commented that many definitions of a general star polygon may be found. I have seen many definitions of a regular star polygon. Often these will assume regularity and not make it explicit; Mathworld is a typical example of this sloppiness. If there are genuine definitions out there, applicable to irregular star polygons, please feel free to give the definition in the article (and of course add the reference). If in doubt, it might be better to post the definition here so we can run over it (for example any definition which discusses Schläfli symbols is likely to apply only to the regular variety, whether or not the author realised this at the time). -- Cheers, Steelpillow (Talk) 19:40, 8 July 2009 (UTC)
replies: text: If your beef is with definitions not covering irregularity, then your lead sentence should state that more explicitly. As it is the sentence doesn't sound very good. Also to be pedantic you'd need a reference for such a strong statement as have never been..., which isn't likely to exist, so it's better to reword to something that can be supported by the available references, not original research. - Taxman Talk 01:03, 9 July 2009 (UTC)
replies: text: I don't like beefing about others' work too much in articles - save that for the discussions. Also to be pedantic, a statement implying that no references exist can hardly be backed up by a reference. OTOH you only need a single one to refute my statement (you originally claimed there are many). Meanwhile, if you can find a better form of words to express what is currently intended, then I have no problem with that. Your remarks have spurred me to have a quick go myself, but there is probably still room for improvement. -- Cheers, Steelpillow (Talk) 19:32, 9 July 2009 (UTC)
thread_title: Irregular remarks in the lead, again

message: It seems a little silly to have two articles about the same subject. Clarityfiend (talk) 00:07, 19 September 2012 (UTC)
replies: text: No - Keep them separte. Mathematically, the idea of a polygon is quite a general idea. Thare are some important sub-types, including for example convex, regular, star and abstract. I'd suggest that each of these important sub-types needs separate treatment in a specialist article (for example abstract polygons are covered in the article on abstract polytopes.— Cheers, Steelpillow (Talk) 18:43, 21 September 2012 (UTC)
replies: text: The articles are about the same subject, but one is from the mathematical perspective, and one from the symbolic. It's obvious to me that these areas need to be treated separately, but in the same article. --St. Nerol (talk) 22:38, 13 January 2013 (UTC)
thread_title:  Merger proposal 

message: User:Steelpillow, your contempt for visualizations is breathtaking.  Incidentally, there is an older version I like better, except for its failure to clearly highlight the compounds. :File:Regular_Star_Polygons-en.svg Tom Ruen (talk) 00:06, 4 February 2015 (UTC)
replies: text: So - you have not yet learned to stop insulting me. And you are gung-ho restoring material without either citation or discussion, which I had cut giving good reason. For example, where is your evidence that "irregular star polygons" are a mathematically significant topic, as opposed to being unexceptional examples of the type known as self-intersecting or coptic polygons? Wikipedia's policy does not accept this as a fanboy page full of ill-informed, uncited enthusiasm and pretty but irrelevant pictures, it is required to stand up mathematically and to be informative of the source material, with an appropriate selection of images to illustrate the text. Do you have a problem with that? — Cheers, Steelpillow (Talk) 10:36, 4 February 2015 (UTC)
thread_title:  Rewrites

message: It's not great, but I decided to be bold and try to split the content to Polygram (geometry), given a clear definition and usage of -gram for both polygons and compounds. Compounds don't really belong under star polygons since they're compounds, while the combined set of star polygons and star figures deserve a name. 
If such a content split is helpful, it will allow this article to be refocused on polygons alone, and it would seem Grünbaum's multiple-wound definition applies to interpretations of {kp/kq} in this article, like his isogonal variations. Tom Ruen (talk) 20:36, 4 February 2015 (UTC)
replies: text: That's all good, I like it. Might it be worth adding a note that {6/2} is also sometimes used to denote the hexagram of two superimposed triangles? — Cheers, Steelpillow (Talk) 12:39, 5 February 2015 (UTC)
thread_title:  Polygrams split? 

message: I added a section on Isotoxal star polygons since Tilings and Patterns talk about it, although I don't have the book at hand at the moment. Tom Ruen (talk) 00:48, 5 February 2015 (UTC)
replies: text: Does Grünbaum refer to these figures as star polygons, or is this new section relying on a single inverted commas reference in a paper about metamorphoses? — Cheers, Steelpillow (Talk) 12:36, 5 February 2015 (UTC)

text: Yes, he says there are two distinct uses for the term "star polygon", and defines the {nα} notation for 2n-gon stars from Kepler. In tiling I think he calls them "hollow tilings" when tiling with the "regular" star forms, where the interior intersections are not considered vertices. Tom Ruen (talk) 18:13, 5 February 2015 (UTC)
replies: text: Then it would be useful to be more explicit about his two definitions. If you can give quotations, together with page references, that would help stop me asking awkward questions and might even make the article adequate. But since you do not have the book to hand, how sure are you about their use of words? Do they really offer both definitions or just some passing remarks that you have taken as such? I do find citing a source that you have not checked somewhat invidious. — Cheers, Steelpillow (Talk) 18:58, 5 February 2015 (UTC)

text: Sorry, I'll try to remember to look later tonight. I've known about the 2 definitions since I read it in 2006 (see above #definition_of_.22star.22_polygons), but I wasn't concerned about the second one since it was regular polygons which interested me. Tom Ruen (talk) 19:14, 5 February 2015 (UTC)

text: I hadn't thought about this before, but most of the isogonal star examples I see may be stellations from the regular polygons, like this isogonal star hexagon, {690°}, is based on a half symmetry of {12/5}. I'm SURE Grünbaum didn't mention this, at least within the tiling book. Tom Ruen (talk) 21:30, 5 February 2015 (UTC)

text: Here's Tilings and Patterns text retyped (errors?) for Steelpillow: Tom Ruen (talk) 07:19, 6 February 2015 (UTC)
thread_title:  Isotoxal star polygons

message: I seen a list of star polygons on the page but it only lists ones stating from 5. That made me thinking, can there be a 4 pointed star polygon? If so, whats it called? Quadragram, Tetragram, Quadrigram? Could someone tell me please? Thanks! 24.150.136.68 (talk) 20:30, 20 April 2017 (UTC)
replies: text: Only regular forms are given here. A 4 sided star polygon might be a compound of two digons, like :File:Regular star figure 2(2,1).svg. Or crossed forms might be what you want, like Rectangle#Crossed_rectangles, so you could have a crossed-square. A concave octagon can be what you want, given at Star_polygon#Simple_isotoxal_star_polygons. Tom Ruen (talk) 20:49, 20 April 2017 (UTC)

text: But what's it called though? and can there be a 3,2, and 1 sided star polygon? 24.150.136.68 (talk) 00:31, 21 April 2017 (UTC)

text: Myself, I'd just call these picture(s) an isotoxal triangular star and isotoxal square star. A 2-sided one (isotoxal digonal star) would be a rhombus. Tom Ruen (talk) 03:01, 21 April 2017 (UTC)

text: Square is more accurate for the relative of exterior points, or convex hull. You could have stretched form like rectangular, rhombic, trapezoidal, irregular. Tom Ruen (talk) 23:13, 21 April 2017 (UTC)

text: Not really. I've only seen the -gram suffice used for n-points, and n crossing edges, and you need at least 4 points for that to occur (as a compound digon), and 5 points needed for a singular path of edges. In other case I'd skip the -gram suffix and say star like 4-pointed star, if there are 4 exterior points and more points inside. So you could call a rhombus a 2-pointed star if you like, but there really can't be a one-pointed star of any sort, unless a single point perhaps! Tom Ruen (talk) 23:08, 21 April 2017 (UTC)
thread_title:  4 pointed star polygon?