Editing Equilateral polygon (section)

==Optimality==
{{main|Reinhardt polygon}}
[[File:Reinhardt 15-gons.svg|thumb|Four Reinhardt pentadecagons]]
When an equilateral polygon is inscribed in a [[Reuleaux polygon]], it forms a [[Reinhardt polygon]]. Among all convex polygons with the same number of sides, these polygons have the largest possible [[perimeter]] for their [[diameter]], the largest possible [[Curve of constant width|width]] for their diameter, and the largest possible width for their perimeter.<ref>{{citation
 | last1 = Hare | first1 = Kevin G.
 | last2 = Mossinghoff | first2 = Michael J.
 | doi = 10.1007/s10711-018-0326-5
 | journal = [[Geometriae Dedicata]]
 | mr = 3933447
 | pages = 1–18
 | title = Most Reinhardt polygons are sporadic
 | volume = 198
 | year = 2019| arxiv = 1405.5233
 | s2cid = 119629098
 }}</ref>