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
Pentagon polygon whose angles are all . To find the number of sides this polygon has, the result is , which is not a whole number. Therefore, a pentagon cannot appear in any tiling made by regular polygons. There are 15 classes of pentagons that can monohedrally tile the plane. None of the pentagons have any symmetry in general, although some have special cases with mirror symmetry. Pentagon In geometry, a pentagon (from the Greek πέντε "pente" and γωνία "gonia", meaning "five" and "angle") is any five-sided polygon or 5-gon. The sum of the internal angles in a simple pentagon is