Editing Combinatorics (section)

===Geometric combinatorics===
[[Image:Icosahedron.svg|150px|thumb|right|An [[icosahedron]].]]

{{Main|Geometric combinatorics}}

Geometric combinatorics is related to [[Convex geometry|convex]] and [[discrete geometry]]. It asks, for example, how many faces of each dimension a [[convex polytope]] can have.  [[Metric geometry|Metric]] properties of polytopes play an important role as well, e.g. the [[Cauchy's theorem (geometry)|Cauchy theorem]] on the rigidity of convex polytopes.  Special polytopes are also considered, such as [[permutohedron|permutohedra]], [[associahedron|associahedra]] and [[Birkhoff polytope]]s. [[Combinatorial geometry]] is a historical name for discrete geometry.

It includes a number of subareas such as [[polyhedral combinatorics]] (the study of [[Face (geometry)|faces]] of [[Convex polyhedron|convex polyhedra]]), [[convex geometry]] (the study of [[convex set]]s, in particular combinatorics of their intersections), and [[discrete geometry]], which in turn has many applications to [[computational geometry]]. The study of [[regular polytope]]s, [[Archimedean solid]]s, and [[kissing number]]s is also a part of geometric combinatorics. Special polytopes are also considered, such as the [[permutohedron]], [[associahedron]] and [[Birkhoff polytope]].