Low-dimensional lattices. VI: Voronoi reduction of three-dimensional lattices. (English) Zbl 0747.11027

Conway, J. H.; Sloane, N. J. A.

Proc. R. Soc. Lond., Ser. A 436, No. 1896, 55-68 (1992).

[Part V, cf. ibid. 426, 211-232 (1989; Zbl 0699.10035).]
The authors give simplified proofs for two old results about lattices in three-dimensional Euclidean space: Any such lattice is “of the first kind” (Voronoi), and there are just five combinatorically distinct possibilities for its Voronoi cell (Fedorov).

Reviewer: H.G.Quebbemann (Oldenburg)

MSC:

11H06	Lattices and convex bodies (number-theoretic aspects)
52C07	Lattices and convex bodies in \(n\) dimensions (aspects of discrete geometry)

Keywords:

Voronoi reduction; lattices in three-dimensional Euclidean space; Voronoi cell

Citations:

Zbl 0699.10035