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).
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) |
Citations:
Zbl 0699.10035Online Encyclopedia of Integer Sequences:
a(n) = 2^n - 1 - n*(n+1)/2.Number of different primitive polyhedral types of Voronoi regions of n-dimensional point lattices.
