Densest Lattice Packings of 3-Polytopes

1999/09/29 by U. Betke, Ulrich Betke, Betke, Ulrich +2
Computer Science · Engineering · Mathematics · #Computational Geometry and Mesh Generation #Optimization and Packing Problems #graph theory and CDMA systems #math.MG #msc:11H06 #msc:52C17 #msc:68U05

paper · pdf · doi:10.48550/arxiv.math/9909172

37 pages

arxiv created 1999/09/29 · arxiv updated 2009/11/30

Abstract

Based on Minkowski's work on critical lattices of 3-dimensional convex bodies we present an efficient algorithm for computing the density of a densest lattice packing of an arbitrary 3-polytope. As an application we calculate densest lattice packings of all regular and Archimedean polytopes.

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