Sphere Packings, Lattices and Groups pp 94-135 | Cite as
Certain Important Lattices and Their Properties
Chapter
Abstract
This chapter describes the properties of a number of important lattices, including the cubic lattice Z n , the root lattices A n , D n , E 6, E 7, E 8, the Coxeter-Todd lattice K 12, the Barnes-Wall lattice Λ16, the Leech lattice Λ24, and their duals. Among other things we give their minimal vectors, densities, covering radii, glue vectors, automorphism groups, expressions for their theta series, and tables of the numbers of points in the first fifty shells. We also include a brief discussion of reflection groups and of the technique of gluing lattices together.
Keywords
Root Lattice Automorphism Group Generator Matrix Weyl Group Minimal Norm
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information
© Springer Science+Business Media New York 1993