Coxeter-Todd Lattice

The complex lattice Lambda_6^omega corresponding to real lattice K_(12) having the densest hypersphere packing (kissing number) in twelve dimensions. The associated automorphism group G_0 was discovered by Mitchell (1914). The order of G_0 is given by


The order of the automorphism group of K_(12) is given by


(Conway and Sloane 1993).

The theta series for the Coxeter-Todd lattice is given in terms of Jacobi elliptic functions by


(OEIS A004010).

Properties of the Coxeter-Todd lattice are implemented in the Wolfram Language as LatticeData["CoxeterTodd", prop].

See also

Barnes-Wall Lattice, Leech Lattice, Theta Series

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Conway, J. H. and Sloane, N. J. A. "The Coxeter-Todd Lattice, the Mitchell Group and Related Sphere Packings." Math. Proc. Camb. Phil. Soc. 93, 421-440, 1983.Conway, J. H. and Sloane, N. J. A. "The 12-Dimensional Coxeter-Todd Lattice K_(12)." §4.9 in Sphere Packings, Lattices, and Groups, 2nd ed. New York: Springer-Verlag, pp. 127-129, 1993.Coxeter, H. S. M. and Todd, J. A. "As Extreme Duodenary Form." Canad. J. Math. 5, 384-392, 1953.Mitchell, H. H. "Determination of All Primitive Collineation Groups in More than Four Variables." Amer. J. Math. 36, 1-12, 1914.Sloane, N. J. A. Sequence A004010/M5478 in "The On-Line Encyclopedia of Integer Sequences."Todd, J. A. "The Characters of a Collineation Group in Five Dimensions." Proc. Roy. Soc. London Ser. A 200, 320-336, 1950.

Referenced on Wolfram|Alpha

Coxeter-Todd Lattice

Cite this as:

Weisstein, Eric W. "Coxeter-Todd Lattice." From MathWorld--A Wolfram Web Resource.

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