Polytopal approximation of elongated convex bodies

Abstract

This paper presents bounds for the best approximation, with respect to the Hausdorff metric, of a convex body $K$ by a circumscribed polytope $P$ with a given number of facets. These bounds are of particular interest if $K$ is elongated. To measure the elongation of the convex set, its isoperimetric ratio $V_j(K{)}^{1/j}{V}_i(K{)}^{-1/i}$ is used.

arXiv comment14 pages, 2 figures