Talk:Triacontagon

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Petrie polygons

The section on Petrie polygons has both implied errors and downright falsehoods. 30-gons do appear as Petrie polygons for certain 4-polytopes that is true. I'm less certain about the 8-polytopes myself, but that may be true. However, by stating "The regular triacontagon ..." the phrasing is certainly implying that the Petrie polygons of the 120-cell and 600-cell are the convex regular 30-gon. The Petrie polygons of the 120-cell and the 600-cell absolutely are not the convex 30-sided polygon. The Petrie polygon of a convex polytope is going to be a skew polygon, never a convex polygon. The observation about the Coxeter plane is correct, the perimeter is the convex {30}, but this just means that it is one of the blend components of the Petrie polygon. There should be two components since the polygon is 4D. (Looking at the Coxeter plane projection I would guess that the other component is {30/11}). The claim that {30/7} is the Petrie polygon of is even more misleading. It's possible that {30/7} is a component of the Petrie polygon, but it's certainly not the Petrie polygon itself.

It's possible that whoever wrote this section has a different definition of Petrie polygon under which these claims are true, something like "the perimeter of the Coxeter plane", although a more complex definition is needed for non-convex polytopes like the {5/2,3,3}. However, the entire section is without references to support any definition like this. Going by the classical definition of Petrie polygon from McMullen & Schulte's Abstract regular polytopes the claims are certainly false as outlined above. I really suspect that this section is WP:OR based on an informal idea of a Petrie polygon. I think the connection between 30-gons and these polytopes is notable but needs to use factual language and proper referencing. AquitaneHungerForce (talk) 23:51, 15 May 2025 (UTC)[reply]