Affine-regular polygon properties of regular polygons are invariant under affine transformations, and affine-regular polygons share the same properties. For instance, an affine-regular quadrilateral can be equidissected into formula_1 equal-area triangles if and only if formula_1 is even, by affine invariance of equidissection and Monsky's theorem on equidissections of squares. More generally an formula_3-gon with formula_4 may be equidissected into formula_1 equal-area triangles if and only if formula_1 is a multiple of formula_3. Affine-regular polygon In geometry, an affine-regular polygon or affinely regular polygon is a polygon that is related to a regular polygon by an affine transformation. Affine transformations include translations, uniform
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