Polytope combinatorics

Summary

Polytope combinatorics, also called polyhedral combinatorics, studies convex polytopes through their faces. It asks how many faces of each dimension a polytope has and how the faces fit together. Its typical questions ask which f-vectors are possible, as in Euler's polyhedron formula, the Dehn–Sommerville equations and the g-theorem. The same name covers the study of the facets of polytopes defined by combinatorial optimization problems, a tool of integer programming.