Editing Polygon (section)

===Equality and symmetry===
* [[Equiangular polygon|Equiangular]]: all corner angles are equal.
* [[Equilateral polygon|Equilateral]]: all edges are of the same length.
* [[Regular polygon|Regular]]: both equilateral and equiangular.
* [[Cyclic polygon|Cyclic]]: all corners lie on a single [[circle]], called the [[circumcircle]].
* [[Tangential polygon|Tangential]]: all sides are tangent to an [[inscribed circle]].
* Isogonal or [[vertex-transitive]]: all corners lie within the same [[symmetry orbit]]. The polygon is also cyclic and equiangular.
* Isotoxal or [[edge-transitive]]: all sides lie within the same [[symmetry orbit]]. The polygon is also equilateral and tangential.

The property of regularity may be defined in other ways: a polygon is regular if and only if it is both isogonal and isotoxal, or equivalently it is both cyclic and equilateral. A non-convex regular polygon is called a ''regular [[star polygon]]''.