Regular polygon Regular polygon In Euclidean geometry, a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygons may be either convex or star. In the limit, a sequence of regular polygons with an increasing number of sides approximates a circle, if the perimeter or area is fixed, or a regular apeirogon (effectively a straight line), if the edge length is fixed. "These properties apply to all regular polygons, whether convex or star." A regular "n"-sided polygon has rotational symmetry of order "n". All vertices of a regular
Coxeter decompositions of hyperbolic polygons of polygons in which any two sharing a side are reflections of each other along that side. The goal of a Coxeter decomposition is to break up a polygon into a composition of congruent triangles reflected on its sides. If triangle ABC can undergo Coxeter decomposition and has angles formula_1, where formula_2 is the number of times the formula_3th angle is broken up, the triangle ABC can be written as formula_4. Several properties of these fundamental polygons are known for hyperbolic triangles. Quadrilaterals may also have Coxeter decompositions. Coxeter decompositions of hyperbolic polygons A Coxeter decomposition of a polygon is