The Contact Polytope of the Leech Lattice

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

• Type: Journal
• Year: 2010
• Where: DCG
• Authors: Mathieu Dutour Sikiric, Achill Schürmann, Frank Vallentin
• Keywords: Contact Polytope, Convex Hull, DCG 2010, Shortest Vectors