The contact polytope of the Leech lattice (complete version)

Published 8 Jun 2009 in math.MG, math.CO, and math.NT | (0906.1427v2)

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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