Abstract
It is well known that ann-dimensional convex body permits a lattice packing of density 1 only if it is a centrally symmetric polytope of at most 2(2n−1) facets. This article concerns itself with the associated stability problem whether a convex body that permits a packing of high density is in some sense close to such a polytope. Several inequalities that address this stability problem are proved. A corresponding theorem for coverings by two-dimensional convex bodies is also proved.
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