ON DIRICHLET-VORONOI CELL Part II. Diagrams

Abstract

This second part of my paper discusses the determination of the DIRICHLET - VORONOI cell of a lattice of dimension n. We give some concrete D-V cells and their automorphism groups, the cells of the lattices An, Dn and En, respectively. These lattices are root lattices to the corresponding finite root systems An, Dn, En. They have an important role in crystallography, physics and differential geometry. We illustrate the diagram method for visualizing very symmetric higher dimensional polytops.