The Minkowski-Weyl Theorem states every polyhedron is
finitely generated and every finitely generated set is a
polyhedron. More precisely,
for two subsets and of , denotes the
Minkowski sum of and :
Thus, every polyhedron has two representations of type (a) and (b), known as (halfspace) H-representation and (vertex) V-representation, respectively. A polyhedron given by H-representation (V-representation) is called H-polyhedron (V-polyhedron).