The six-dimensional Delaunay polytopes
Abstract
Given a lattice L, a full dimensional polytope P is called a Delaunay polytope if the set of its vertices is S L with S being an empty sphere of the lattice. Extending our previous work DD-hyp on the hypermetric cone HYP7, we classify the six-dimensional Delaunay polytopes according to their combinatorial type. The list of 6241 combinatorial types is obtained by a study of the set of faces of the polyhedral cone HYP7.
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