The six-dimensional Delaunay polytopes

Authors:
Mathieu Dutour
Affiliations:
ENS, Paris and Hebrew University, Jerusalem, Israel
Venue:
European Journal of Combinatorics - Special issue on arithmétique et combinatoire
Year:
2004

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Abstract

Given a lattice L, a 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 (Available from http://il.arXiv.org/abs/math.MG/0108177) on the hypermetric cone HY P7, 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 HY P7.