24 November 2011 UTC My apology if you find a personal attack in my more recent comment above I have re read it and can still find none You argue that we should make the definition of polygon consistent with what the lay public is likely to encounter and study while I believe that the elementary logic of physical objects is best used in the introductory lead That looks like agreement to me Where we seem to differ is that you regard this as calling for a Euclidean mathematical definition while I do not believe that the lay person has sufficient mathematical appreciation for that to be appropriate to the article lead As to the actual content the lead grew historically as a result of several contributors thrashing out our differing approaches What emerged should not be treated lightly or substantially edited without prior agreement I am happy to discuss the rest of your proposal and no doubt others will chip in to help reach a consensus I did restore a little of what you wrote but in the mean time let us not play ping pong with the page itself On the matter of references Regular polytopes and Convex polytopes are widely read works which can hardly be described as specialised they are indeed precisely what this lay person encountered and studied Some others which I referenced are original sources which out of respect to you as a professional mathematician I would not pull away from drawing to your attention Others do move beyond a Euclidean treatment and were there simply to make the point which begins the subsequent paragraph More directly relevant is the issue that most lay people would regard a pentagram as a star polygon recognised as such since the days of Archimedes but excluded by the definition you gave which is more formally understood as a simple polygon While mathematicians such as Gr nbaum and yourself might choose to frequently omit descriptors such as simple or convex in treatments of these objects Gr nbaum explicitly yourself implicitly a general introduction to the subject can take no such luxury The article lead should conform as far as is possible to the lay person s preconceptions whereby polygons may be divided into those which self intersect and those which do not With that proviso if you have ideas for significant changes to the article lead I would hope you can share them with us first Cheers Talk 20 34