  40 years ago, Conway and Sloane proposed using the highly symmetrical
Coxeter-Todd lattice $K_{12}$ for quantization, and estimated its second
moment. Since then, all published lists identify $K_{12}$ as the best
12-dimensional lattice quantizer. Surprisingly, $K_{12}$ is not optimal: we
construct two new 12-dimensional lattices with lower normalized second moments.
The new lattices are obtained by gluing together 6-dimensional lattices.
