A 24-D Euclidean lattice. An Automorphism of the Leech lattice modulo a center of two leads to the
Conway Group . Stabilization of the 1- and 2-D sublattices leads to the
Conway Groups and , the Higman-Sims Group *HS* and the McLaughlin Group
*McL*.

The Leech lattice appears to be the densest Hypersphere Packing in 24-D, and results in each Hypersphere touching 195,560 others.

**References**

Conway, J. H. and Sloane, N. J. A. ``The 24-Dimensional Leech Lattice ,'' ``A Characterization of the Leech Lattice,''
``The Covering Radius of the Leech Lattice,'' ``Twenty-Three Constructions for the Leech Lattice,'' ``The Cellular of the Leech Lattice,''
``Lorentzian Forms for the Leech Lattice.''
§4.11, Ch. 12, and Chs. 23-26 in *Sphere Packings, Lattices, and Groups, 2nd ed.*
New York: Springer-Verlag, pp. 131-135, 331-336, and 478-526, 1993.

Leech, J. ``Notes on Sphere Packings.'' *Canad. J. Math.* **19**, 251-267, 1967.

Wilson, R. A. ``Vector Stabilizers and Subgroups of Leech Lattice Groups.'' *J. Algebra* **127**, 387-408, 1989.

© 1996-9

1999-05-26