Rank 1 forms, closed zones and laminae
Journal de théorie des nombres de Bordeaux, Tome 14 (2002) no. 1, pp. 103-112.

Étant donné un réseau, nous construisons une équivalence entre des zones fermées du polytope de Voronoï correspondant, des sections hyperplanes convenables de la partition de Delaunay, et des formes quadratiques de rang 1 qui sont des rayons extrêmes pour les domaines de type L correspondants.

For a given lattice, we establish an equivalence between closed zones for the corresponding Voronoï polytope, suitable hyperplane sections of the corresponding Delaunay partition, and rank 1 quadratic forms which are extreme rays for the corresponding L-type domain.

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Deza, Michel; Grishukhin, Viatcheslav. Rank $1$ forms, closed zones and laminae. Journal de théorie des nombres de Bordeaux, Tome 14 (2002) no. 1, pp. 103-112. http://www.numdam.org/item/JTNB_2002__14_1_103_0/

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