The six-dimensional Delaunay polytopes

Details The six-dimensional Delaunay polytopes The six-dimensional Delaunay polytopes

2002-12-27

arxiv.org/abs/math/0212353v1

Mathematics

Metric Geometry

14 pages, no figure

Scientific paper

Given a lattice $L$, a full dimensional polytope $P$ is called a {\em Delaunay polytope} if the set of its vertices is $S\cap L$ with $S$ being an {\em empty sphere} of the lattice. Extending our previous work \cite{DD-hyp} on the {\em hypermetric cone} $HYP_7$, we classify the six-dimensional Delaunay polytopes according to their {\em combinatorial type}. The list of 6241 combinatorial types is obtained by a study of the set of faces of the polyhedral cone $HYP_7$.

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