On Canonical Representations of Convex Polyhedra

Every convex polyhedron in the Euclidean space Rd admits both H-representation and V-representation. When working with convex polyhedra, in particular largescale ones in high dimensions, it is useful to have a canonical representation that is minimal and unique up to some elementary operations. Such a representation allows one to compare two H-polyhedra or two V-polyhedra efficiently. In this paper, we define such representations that are simple and can be computed in polynomial time. The key ingredients are redundancy removal for linear inequality systems and affine transformations of polyhedra.