Large convex hull problems

Every convex polytope has both a vertex and a halfspace description. The complexity of translating from the vertices to the halfspaces (convex hull) or vice versa (vertex enumeration) remains an important open problem in computational geometry. In this note we present families of hard polytopes for algorithms using pivoting, constraint insertion, and triangulation, and discuss techniques for estimating the difficulty of a convex hull or vertex enumeration instance.