Densest packings of typical convex sets are not lattice-like

Abstract

We show that if P is a convex polygon which has no parallel sides, then the densest packing of the plane with congruent copies of P is not lattice-like. As a corollary we obtain that, in the sense of Baire categories, for most convex disks densest packing is not lattice-like. © 1995 Springer-Verlag New York Inc.