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 the vertex figure. Unlike the case for Euclidean polytopes, an abstract polytope with regular facets and vertex figures "may or may not" be regular itself – for example, the square pyramid, all of whose facets and vertex figures are regular abstract polygons. The classical vertex figure will, however, be a realisation of the abstract one. The traditional way to construct a regular polygon, or indeed any other figure on the plane, is by compass and straightedge. Constructing some regular polygons in this way is very simple (the easiest is perhaps the equilateral triangle), some are more complex, and some are