Geometric combinatorics
Geometric combinatorics is a branch of mathematics in general and combinatorics in particular. It includes a number of subareas such as polyhedral combinatorics, convex geometry, and discrete geometry, which in turn has many applications to computational geometry. Other important areas include metric geometry of polyhedra, such as the Cauchy theorem on rigidity of convex polytopes. The study of regular polytopes, Archimedean solids, and kissing numbers is also a part of geometric combinatorics. Special polytopes are also considered, such as the permutohedron, associahedron and Birkhoff polytope.
