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What is convex polytope/polyhedron?

A subset $ P$ of $ R^d$ is called a convex polyhedron if it is the set of solutions to a finite system of linear inequalities, and called convex polytope if it is a convex polyhedron and bounded. When a convex polyhedron (or polytope) has dimension $ k$, it is called a $ k$-polyhedron ($ k$-polytope). For the sequel, we might omit convex for convex polytopes and polyhedra, and call them simply polytopes and polyhedra.

Komei Fukuda 2004-08-26