# 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 and non-uniform scaling, reflections, rotations, shears, and other similarities and some, but not all linear maps.

All triangles are affine-regular. In other words, all triangles can be generated by applying affine transformations to an equilateral triangle. A quadrilateral is affine-regular if and only if it is a parallelogram, which includes rectangles and rhombuses as well as squares. In fact, affine-regular polygons may be considered a natural generalization of parallelograms.^{[1]}

Many 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 equal-area triangles if and only if is even, by affine invariance of equidissection and Monsky's theorem on equidissections of squares.^{[2]} More generally an -gon with may be equidissected into equal-area triangles if and only if is a multiple of .^{[3]}