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

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