# Polygon

In elementary geometry, a **polygon** /ˈpɒlɪɡɒn/ is a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed chain or *circuit*. These segments are called its *edges* or *sides*, and the points where two edges meet are the polygon's *vertices* (singular: vertex) or *corners*. The interior of the polygon is sometimes called its *body*. An ** n-gon** is a polygon with

*n*sides. A polygon is a 2-dimensional example of the more general polytope in any number of dimensions.

The basic geometrical notion of a polygon has been adapted in various ways to suit particular purposes. Mathematicians are often concerned only with the bounding closed polygonal chain and with **simple polygons** which do not self-intersect, and they often define a polygon accordingly. A polygonal boundary may be allowed to intersect itself, creating **star polygons**. Geometrically two edges meeting at a corner are required to form an angle that is not straight (180°); otherwise, the line segments may be considered parts of a single edge; however mathematically, such corners may sometimes be allowed. These and other generalizations of polygons are described below.

5comments