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
Regular polytope providing a technique that allows the abstract regular polytope to be constructed from its symmetry group in a standard and straightforward manner. For examples of polygons in nature, see: Each of the Platonic solids occurs naturally in one form or another: Regular polytope In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry. All its elements or "j"-faces (for all 0 ≤ "j" ≤ "n", where "n" is the dimension of the polytope) — cells, faces and so on — are also transitive on the symmetries