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

[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).

MSC:

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

Citations:

Zbl 0699.10035
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