Star polygons in art and culture Star polygons in art and culture Star polygons and polygonal compounds are the basis for numerous figures of significance in arts and culture. The figure may be the border or interior of the polygon, or one or more closed polygonal paths that include all of the border and also have some legs crossing the interior. Impressions of astronomical stars provide the term, but specific uses may exploit the connection or not. Stars often represent the unity of states within a country when they are used as a part of the flag. The five-pointed star, if drawn with points of equal
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