The Surface Area Deviation of the Euclidean Ball and a Polytope

TL;DR

This paper investigates the bounds on how well convex bodies can be approximated by arbitrarily positioned polytopes with a fixed number of vertices, focusing on symmetric surface area deviation.

Contribution

It provides new upper and lower bounds for the approximation of convex bodies by polytopes with a fixed number of vertices in symmetric surface area deviation.

Findings

Established bounds for approximation quality

Extended understanding beyond inscribed or circumscribed polytopes

Focused on arbitrary positioning of polytopes

Abstract

While there is extensive literature on approximation of convex bodies by inscribed or circumscribed polytopes, much less is known in the case of generally positioned polytopes. Here we give upper and lower bounds for approximation of convex bodies by arbitrarily positioned polytopes with a fixed number of vertices in the symmetric surface area deviation.