The local optimality of the double lattice packing

Abstract

This paper introduces a technique for proving the local optimality of packing configurations. Applying this technique to a general convex polygon, we prove that the construction of the optimal double lattice packing by Kuperberg and Kuperberg is also locally optimal in the full space of packings.

Source files include Mathematica notebooks implementing calculations

References in corpus (4)

• Improved sphere packing lower bounds from Hurwitz lattices
• Upper bound on the packing density of regular tetrahedra and octahedra
• The 3-ball is a local pessimum for packing
• Pessimal packing shapes

Cited by in corpus (1)

• Densest plane group packings of regular polygons