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 polyhedron valleys, enabling them to construct three infinite folded surfaces which they called regular skew polyhedra. Coxeter offered a modified Schläfli symbol {l,m|n} for these figures, with {l,m} implying the vertex figure, with "m" regular "l"-gons around a vertex. The "n" defines "n"-gonal "holes". Their vertex figures are regular skew polygons, vertices zig-zagging between two planes. Finite regular skew polyhedra exist in 4-space. These finite regular skew polyhedra in 4-space can be seen as a subset of the faces of uniform 4-polytopes. They have planar regular polygon faces, but regular skew polygon vertex figures. Two dual solutions are related to the