Infinite series of extreme Delaunay polytopes

  • Authors:

  • V. P. Grishukhin

  • Affiliations:

  • CEMI, Russian Academy of Sciences, Nakhimovvkki Prospect, Moscow, Russia

  • Venue:
  • European Journal of Combinatorics
  • Year:
  • 2006

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Abstract

Recently, Rybnikov and Erdahl [R. Erdahl, K. Rybnikov, Supertopes, Supertopes.pdf at http:// faculty.uml.edu/krybnikov/, 2002] constructed an infinite series of asymmetric extreme lattice Delaunay polytopes PER(n) for dimensions n ≥ 6. Dutour [M. Dutour, An infinite series of extreme Delaunay polytopes, European J. Combin. (2003) (in press)] constructed another infinite series of asymmetric extreme Delaunay polytopes PDu(n) for all even dimensions n ≥ 6. An analysis of the first series allows one to construct two two-parametric series P(n; t) and PA(n; t) of asymmetric extreme Delaunay polytopes such that P(n; 1) = PER(n). In addition, for each asymmetric extreme Delaunay potytope P of dimension n, an explicit construction of a symmetric extreme Delaunay potytope of dimension n + 1 having P as a section is given.