The contact polytope of the Leech lattice (complete version)
Metric Geometry
2010-10-12 v2 Combinatorics
Number Theory
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.
Cite
@article{arxiv.0906.1427,
title = {The contact polytope of the Leech lattice (complete version)},
author = {Mathieu Dutour Sikiric and Achill Schuermann and Frank Vallentin},
journal= {arXiv preprint arXiv:0906.1427},
year = {2010}
}
Comments
(v2) 7 pages (part I), 13 pages (part II), 1 figure, 2 tables, part I to appear in Discr. Comp. Geom