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Adjacency method for extreme Delaunay polytopes

Mathieu Dutour
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Abstract

The {\em hypermetric cone} is defined as the cone of semimetrics satisfying the {\em hypermetric inequalities}. Every {\em Delaunay polytope} corresponds to a ray of this polyhedral cone. The Delaunay polytopes, which correspond to extreme rays are called {\em extreme}. We use this polyhedral cone and the {\em 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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Mathieu Dutour. 2004-01-02. Adjacency method for extreme Delaunay polytopes. https://arxiv.org/abs/math/0401004

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