## ::Polygon

### ::concepts

Polygon::books    Polygons::sides    Angle::regular    Which::simple    Google::interior    Theta::plane

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Some polygons of different kinds: open (excluding its boundary), bounding circuit only (ignoring its interior), closed (both), and self-intersecting with varying densities of different regions.

In elementary geometry, a polygon {{#invoke:IPAc-en|main}} 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.

Polygon sections
Intro   Etymology   Classification  Properties and Formulas  Generalizations of polygons  Naming polygons  History  Polygons in nature  Polygons in computer graphics  See also  References  External links

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