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The Contact Polytope of the Leech Lattice

Abstract

The contact polytope of a lattice is the convex hull of its shortest vectors. In this paper we classify the facets of the contact polytope of the Leech lattice up to symmetry. There are 1,197,362,269,604,214,277,200 many facets in 232 orbits.

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Correspondence to Frank Vallentin.

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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Dutour Sikirić, M., Schürmann, A. & Vallentin, F. The Contact Polytope of the Leech Lattice. Discrete Comput Geom 44, 365体育网站904–911 (2010). http://doi.org/10.1007/s00454-010-9266-z

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Keywords

  • Leech lattice
  • Contact polytope
  • Conway groups
  • Voronoi cell