The polyhedral combinatorium is a branch of mathematics, within combinatorics and discrete geometry, which studies the problems of counting and describing the faces of convex polyhedra and convex polytopes of higher dimensions.
Research in polyhedral combinatorics falls into two distinct areas. Mathematicians in this area study the combinatorics of polytopes; for example, look for the inequalities that describe the relationships between vertex numbers, edges, and faces of higher dimensions in arbitrary polytopes or in certain important subclasses of polytopes, and also study other combinatorial characteristics of polytopes such as their connectivity and diameter (number of steps necessary to reach any vertex from any other vertex). In addition, many computer scientists use the phrase "polyhedral combinatorics" to describe research in precise descriptions of the faces of certain specific polytopes (especially polytopes 0-1, whose vertices are subsets of a hypercube) / p>
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