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
Skew apeirogon they can be called quasiregular. Example quasiregular skew apeirogons can be seen in the Euclidean tilings as truncated Petrie polygons in truncated regular tilings: In hyperbolic geometry, regular skew apeirogons are similarly found like in the Euclidean plane. Hyperbolic regular skew apeirogons also exist as Petrie polygon zig-zagging edge paths on all of the regular tilings of the hyperbolic plane. And again like Euclidean space, hyperbolic quasiregular skew apeirogons can be constructed as truncated petrie polygons within the edges of a truncated regular tiling. A helical skew apeirogon can exist in three dimensions, where the vertices can be seen as