Editing Polygon (section)

==Classification==
[[File:Polygon types.svg|thumb|right|300px|Some different types of polygon]]

===Number of sides===
Polygons are primarily classified by the number of sides.

===Convexity and intersection===
Polygons may be characterized by their convexity or type of non-convexity:
* [[convex polygon|Convex]]: any line drawn through the polygon (and not tangent to an edge or corner) meets its boundary exactly twice. As a consequence, all its interior angles are less than 180°. Equivalently, any line segment with endpoints on the boundary passes through only interior points between its endpoints. This condition is true for polygons in any geometry, not just Euclidean.<ref>{{citation |last=Magnus |first=Wilhelm |author-link=Wilhelm Magnus |title=Noneuclidean tesselations and their groups |series=Pure and Applied Mathematics |volume=61 |publisher=Academic Press |year=1974|url=
https://www.sciencedirect.com/bookseries/pure-and-applied-mathematics/vol/61/suppl/C|page=37}}</ref>
* Non-convex: a line may be found which meets its boundary more than twice. Equivalently, there exists a line segment between two boundary points that passes outside the polygon.
* [[simple polygon|Simple]]: the boundary of the polygon does not cross itself. All convex polygons are simple.
* [[Concave polygon|Concave]]: Non-convex and simple. There is at least one interior angle greater than 180°.
* [[Star-shaped polygon|Star-shaped]]: the whole interior is visible from at least one point, without crossing any edge. The polygon must be simple, and may be convex or concave. All convex polygons are star-shaped.
* [[list of self-intersecting polygons|Self-intersecting]]: the boundary of the polygon crosses itself. The term ''complex'' is sometimes used in contrast to ''simple'', but this usage risks confusion with the idea of a ''[[Complex polytope|complex polygon]]'' as one which exists in the complex [[Hilbert space|Hilbert]] plane consisting of two [[complex number|complex]] dimensions.
* [[Star polygon]]: a polygon which self-intersects in a regular way. A polygon cannot be both a star and star-shaped.

===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]]''.

===Miscellaneous===
* [[Rectilinear polygon|Rectilinear]]: the polygon's sides meet at right angles, i.e. all its interior angles are 90 or 270 degrees.
* [[Monotone polygon|Monotone]] with respect to a given line ''L'': every line [[Orthogonal (geometry)|orthogonal]] to L intersects the polygon not more than twice.