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
Rectification (geometry) 2r{p,q...}. For polyhedra, a birectification creates a dual polyhedron. Higher degree rectifications can be constructed for higher dimensional polytopes. In general an n-rectification truncates "n-faces" to points. If an n-polytope is (n-1)-rectified, its facets are reduced to points and the polytope becomes its dual. There are different equivalent notations for each degree of rectification. These tables show the names by dimension and the two type of facets for each. Facets are edges, represented as {2}. Facets are regular polygons. Facets are regular or rectified polyhedra. Facets are regular or rectified 4-polytopes. Rectification (geometry) In Euclidean geometry, rectification or complete-truncation is