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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Springer
Discrete and Computational Geometry
Spinoza prijs Lex Schrijver
Networks and Optimization

Dutour Sikirić, M., Schuermann, A., & Vallentin, F. (2010). The contact polytope of the Leech lattice. Discrete and Computational Geometry, 44(4), 904–911.