Equidissection Equidissection In geometry, an equidissection is a partition of a polygon into triangles of equal area. The study of equidissections began in the late 1960s with Monsky's theorem, which states that a square cannot be equidissected into an odd number of triangles. In fact, most polygons cannot be equidissected at all. Much of the literature is aimed at generalizing Monsky's theorem to broader classes of polygons. The general question is: Which polygons can be equidissected into how many pieces? Particular attention has been given to trapezoids, kites, regular polygons, centrally symmetric polygons, polyominos, and hypercubes. Equidissections do not have many
Regular polygon (of order 2"n"): "D", "D", "D", ... It consists of the rotations in "C", together with reflection symmetry in "n" axes that pass through the center. If "n" is even then half of these axes pass through two opposite vertices, and the other half through the midpoint of opposite sides. If "n" is odd then all axes pass through a vertex and the midpoint of the opposite side. All regular simple polygons (a simple polygon is one that does not intersect itself anywhere) are convex. Those having the same number of sides are also similar. An "n"-sided convex regular polygon