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
Euclidean tilings by convex regular polygons uniformity which requires edge-to-edge regular polygons. Such isogonal tilings are actually topologically identical to the uniform tilings, with different geometric proportions. Euclidean and general tiling links: Euclidean tilings by convex regular polygons Euclidean plane tilings by convex regular polygons have been widely used since antiquity. The first systematic mathematical treatment was that of Kepler in his "Harmonices Mundi" (Latin: "The Harmony of the World", 1619). Following Grünbaum and Shephard (section 1.3), a tiling is said to be "regular" if the symmetry group of the tiling acts transitively on the "flags" of the tiling, where a flag is a triple consisting