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.