99-18
Densest lattice packings of 3-polytopes
by Betke, Ulrich; Henk, Martin
Preprint series: 99-18, Preprints
- MSC:
- 52C17 Packing and covering in $n$ dimensions, See also {05B40, 11H31}
- 11H06 Lattices and convex bodies, See also {11P21, 52C05, 52C07}
- 68U05 Computer graphics; computational geometry, See also {65Y25}
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.
Keywords: lattice packings, critical lattice, polytopes
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