Adjacency method for extreme Delaunay polytopes
Abstract
The hypermetric cone is defined as the cone of semimetrics satisfying the hypermetric inequalities. Every Delaunay polytope corresponds to a ray of this polyhedral cone. The Delaunay polytopes, which correspond to extreme rays are called extreme. We use this polyhedral cone and the closest vector problem to present a new technique that allow to find, from a given extreme Delaunay polytope, some new ones. Then, we show some examples of applications of this technique in low-dimensions.
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