engleski

Delaunay polytopes in lattices

A delaunay polytope of a lattice L is a polytope, which is defined as the convex hull S inter L with S a sphere that does not contain lattices points in its interior. A Delaunay polytope is perfect if the set S inter L determines the lattice up to isometry. We introduce here the theory of the Erdahl cone to describe such polytopes. The Delaunay polytopes of a lattice L determine the covering radiusand we describe a new theory of covering maxima, which uses corresponding notions of perfectness and eutaxy for Delaunay polytopes.

lattices; reduction; polytopes

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