Editing Equilateral polygon (section)

==Examples==

All [[regular polygon]]s and [[isotoxal polygon|edge-transitive polygon]]s are equilateral. When an equilateral polygon is non-crossing and [[Cyclic polygon|cyclic]] (its vertices are on a circle) it must be regular. An equilateral [[quadrilateral]] must be convex; this polygon is a [[rhombus]] (possibly a [[square]]).

{{multiple image|total_width=360|image1=5-gon equilateral 01.svg|caption1=Convex equilateral pentagon|image2=5-gon equilateral 03.svg|caption2=Concave equilateral pentagon}}
A convex [[equilateral pentagon]] can be described by two consecutive angles, which together determine the other angles. However, equilateral pentagons, and equilateral polygons with more than five sides, can also be concave, and if concave pentagons are allowed then two angles are no longer sufficient to determine the shape of the pentagon.

A [[tangential polygon]] (one that has an [[incircle]] tangent to all its sides) is equilateral if and only if the alternate angles are equal (that is, angles 1, 3, 5, ... are equal and angles 2, 4, ... are equal). Thus if the number of sides ''n'' is odd, a tangential polygon is equilateral if and only if it is regular.<ref>{{citation|last=De Villiers|first=Michael|title=Equi-angled cyclic and equilateral circumscribed polygons|journal=[[Mathematical Gazette]]|volume=95|date=March 2011|pages=102–107|doi=10.1017/S0025557200002461|url=http://frink.machighway.com/~dynamicm/equi-anglecyclicpoly.pdf|access-date=2015-04-29|archive-date=2016-03-03|archive-url=https://web.archive.org/web/20160303172114/http://frink.machighway.com/~dynamicm/equi-anglecyclicpoly.pdf|url-status=dead}}.</ref>