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A convex polytope is a special case of a polytope, having the additional property that it is also a convex set contained in the n-dimensional Euclidean space \mathbb{R}^n. M
In geometry, a polyhedron (: polyhedra or polyhedrons; ) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices.A convex polyhedron is a polyhedron th
In computer science, canonicalization (sometimes standardization or normalization) is a process for converting data that has more than one possible representation into a "standard", "normal", or can
Every convex polyhedron in Rd admits both H- and V-representations. In both cases, a representation is defined to be canonical if it is minimal and unique up to simple transformations. In general, canonical H- and V-representations are discussed separately, resulting in two different definitions. In contrast, the duality of polyhedral cones suggests a possible "unification" of the two types of canonical representations. In this paper, we describe a family of canonical representations, the dfnS-canonical representations, which definitions are the same for both H- and V-representation. We show that every S-canonical V-representation coincide with the S-canonical H-representation of a certain polyhedron. As a consequence, methods developed to determine S-canonical H-representations can be applied successfully in V-representation.