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 first flag to the second. This is equivalent to the tiling being an edge-to-edge tiling by congruent regular polygons. There must be six equilateral triangles, four squares or three regular hexagons at a vertex, yielding the three regular tessellations. Vertex-transitivity means that for every pair of vertices there is a symmetry operation mapping the first vertex to the second. If the requirement of flag-transitivity is relaxed to one of vertex-transitivity, while the condition that the tiling is edge-to-edge is kept, there are eight additional tilings possible, known as "Archimedean", "uniform" or "semiregular" tilings. Note that there are two mirror image