Infinite serie of extreme Delaunay polytopes

Details Infinite serie of extreme Delaunay polytopes Infinite serie of extreme Delaunay polytopes

2003-05-14

arxiv.org/abs/math/0305196v1

Mathematics

Metric Geometry

3 pages

Scientific paper

A Delaunay polytope $P$ is said to be {\em extreme} if the only (up to isometries) affine bijective transformations $f$ of $\R^n$, for which $f(P)$ is again a Delaunay polytope, are the homotheties. This notion was introduced in \cite{DGL92}; also some examples in dimension 1, 6, 7, 15, 16, 22, 23 were constructed and it was proved that in dimension less than 6 there are no extreme Delaunay polytopes, except the segment. In this note, for every $n\geq 6$ we build an extreme Delaunay polytope $ED_n$ of dimension $n$.

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