Coxeter–Todd lattice

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 analogous to the Barnes–Wall lattice. The automorphism group of the Coxeter–Todd lattice has order 2¹⁰·3⁷·5·7=78382080, and there are 756 vectors in this lattice of norm 4 (the shortest nonzero vectors in this lattice).

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