Finite Packings by Translates of Convex Bodies

Abstract

Let K be a convex body (i.e., a compact convex set with nonempty interior) in d-dimensional Euclidean space \(\mathbb{E}^d\), d ≥ 2. Then the Hadwiger number H(K) of K is the largest number of non-overlapping translates of K that can all touch K. An elegant observation of Hadwiger [154] is the following.