Perfect Delaunay polytopes in low dimensions.

Dutour Sikirić, Mathieu; Erdahl, Robert; Rybnikov, Konstantin

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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.