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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Cornell University Library
arXiv.org e-Print archive
Networks and Optimization

Dutour Sikirić, M., Schuermann, A., & Vallentin, F. (2009). The contact polytope of the Leech lattice. arXiv.org e-Print archive. Cornell University Library .