The cell structures of certain lattices. (English) Zbl 0738.52014

Conway, John H.; Sloane, Neil J. A.

Miscellanea mathematica, Festschr. H. Götze, 71-107 (1991).

[For the entire collection see Zbl 0723.00017.]
This paper is not only an extension to Chapter 21 of the authors’ book “Sphere Packings, Lattices and Groups”, Springer, New York (1988; Zbl 0634.52002) but it gives a good readable survey of new results concerning the most important lattices in Euclidean \(n\)-spaces \((n<8)\) \(A_ n\), \(D_ n\), \(E_ n\) and their duals. The authors determine the cell structures of these lattices and their Voronoi and Delaunay polytopes in a uniform manner.

Reviewer: E.Hertel (Jena)

MSC:

52C07	Lattices and convex bodies in \(n\) dimensions (aspects of discrete geometry)
51M20	Polyhedra and polytopes; regular figures, division of spaces

Keywords:

sphere packings; survey; lattices in Euclidean \(n\)-spaces; duals; Voronoi and Delaunay polytopes

Software:

MINOS