Adjacency method for extreme Delaunay polytopes
  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. 
Mathieu Dutour