Regular polygon is denoted by its Schläfli symbol {"n"}. For "n" < 3, we have two degenerate cases: In certain contexts all the polygons considered will be regular. In such circumstances it is customary to drop the prefix regular. For instance, all the faces of uniform polyhedra must be regular and the faces will be described simply as triangle, square, pentagon, etc. For a regular convex "n"-gon, each interior angle has a measure of: and each exterior angle (i.e., supplementary to the interior angle) has a measure of formula_5 degrees, with the sum of the exterior angles equal to 360 degrees or
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