Densest Lattice Packings of 3-Polytopes

Details Densest Lattice Packings of 3-Polytopes Densest Lattice Packings of 3-Polytopes

1999-09-29

arxiv.org/abs/math/9909172v1

Mathematics

Metric Geometry

37 pages

Scientific paper

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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