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Densest lattice packings of 3-polytopes

by Betke, Ulrich, Henk, Martin.

Series: 1999-18, Preprints

52C17 Packing and covering in $n$ dimensions
11H06 Lattices and convex bodies
68U05 Computer graphics; computational geometry

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.

lattice packings, critical lattice, polytopes