In mathematics, the Coxeter–Todd lattice K12, discovered by Coxeter and Todd (1953), is a 12-dimensional even integral lattice of discriminant 36 with no norm-2 vectors. It is the sublattice of the Leech lattice fixed by a certain automorphism of order 3, and is similar to the Barnes–Wall lattice.
The Coxeter–Todd lattice can be made into a 6-dimensional lattice self dual over the Eisenstein integers. The automorphism group of this complex lattice has index 2 in the full automorphism group of the Coxeter–Todd lattice and is a complex reflection group (number 34 on the list) with structure 6.PSU4(F3).2, called the Mitchell group.
- Conway, J. H.; Sloane, N. J. A. (1983), "The Coxeter–Todd lattice, the Mitchell group, and related sphere packings", Math. Proc. Cambridge Philos. Soc., 93 (3): 421–440, doi:10.1017/S0305004100060746, MR 0698347
- Conway, John Horton; Sloane, Neil J. A. (1999), Sphere Packings, Lattices and Groups, Grundlehren der Mathematischen Wissenschaften, 290 (3rd ed.), Berlin, New York: Springer-Verlag, ISBN 978-0-387-98585-5, MR 0920369
- Coxeter, H. S. M.; Todd, J. A. (1953), "An extreme duodenary form", Canadian J. Math., 5: 384–392, doi:10.4153/CJM-1953-043-4, MR 0055381
- Scharlau, Rudolf; Venkov, Boris B. (1995), "The genus of the Coxeter-Todd lattice", Preprint
- Coxeter–Todd lattice in Sloane's lattice catalogue