Infinite serie of extreme Delaunay polytopes

  • Authors:

  • Mathieu Dutour

  • Affiliations:

  • LIGA, ENS/CNRS, Paris, France and Hebrew University, Jerusalem, Israel

  • Venue:
  • European Journal of Combinatorics
  • Year:
  • 2005

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Abstract

A Delaunay polytope P is said to be extreme if the only (up to isometries) affine bijective transformations f of Rn, for which f(P) is again a Delaunay polytope, are the homotheties. This notion was introduced in (Sets, Graphs and Numbers, Budapest (Hungary) (1991); Colloquia Mathematica Societatis János Bolyai 60 (1992) 157); also some examples in dimension 1, 6, 7, 15, 16, 22, 23 were constructed and it was proved there, that in dimension less than 6 there are no extreme Delaunay polytopes, except the segment. In this note, for every n ≥ 6 we build an extreme Delaunay polytope E Dn of dimension n.