Editing Polygon (section)

==Generalizations==

The idea of a polygon has been generalized in various ways. Some of the more important include:
* A [[spherical polygon]] is a circuit of arcs of great circles (sides) and vertices on the surface of a sphere. It allows the [[digon]], a polygon having only two sides and two corners, which is impossible in a flat plane. Spherical polygons play an important role in [[cartography]] (map making) and in [[Wythoff's construction]] of the [[uniform polyhedra]].
* A [[skew polygon]] does not lie in a flat plane, but zigzags in three (or more) dimensions. The [[Petrie polygon]]s of the regular polytopes are well known examples.
* An [[apeirogon]] is an infinite sequence of sides and angles, which is not closed but has no ends because it extends indefinitely in both directions.
* A [[skew apeirogon]] is an infinite sequence of sides and angles that do not lie in a flat plane.
* A [[polygon with holes]] is an area-connected or multiply-connected planar polygon with one external boundary and one or more interior boundaries (holes).
* A [[Complex polytope|complex polygon]] is a [[configuration (polytope)|configuration]] analogous to an ordinary polygon, which exists in the [[complex plane]] of two [[real number|real]] and two [[imaginary number|imaginary]] dimensions.
* An [[abstract polytope|abstract polygon]] is an algebraic [[partially ordered set]] representing the various elements (sides, vertices, etc.) and their connectivity. A real geometric polygon is said to be a ''realization'' of the associated abstract polygon. Depending on the mapping, all the generalizations described here can be realized.
* A [[polyhedron]] is a three-dimensional solid bounded by flat polygonal faces, analogous to a polygon in two dimensions. The corresponding shapes in four or higher dimensions are called [[polytope]]s.<ref>Coxeter (3rd Ed 1973)</ref> (In other conventions, the words ''polyhedron'' and ''polytope'' are used in any dimension, with the distinction between the two that a polytope is necessarily bounded.<ref>[[Günter Ziegler]] (1995). "Lectures on Polytopes". Springer ''Graduate Texts in Mathematics'', {{isbn|978-0-387-94365-7}}. p. 4.</ref>)