On the duality of canonical representations rules for convex polyhedra

Stefano Picozzi
2005
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On duality of canonical representations

Stefano Picozzi

Every convex polyhedron in

R^d

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.

2004