Delaunay polytopes of cut lattices Original Research Article

We continue the study of the lattice imagen generated by cuts of the complete graph on a set Vn of n vertices. The lattice imagen spans an image space of all functions defined on a set En of all unordered pairs of the set Vn. Baranovski proves that symmetric Delaunay polytopes of a lattice L are completely described by classes of the quotient image. We show that a class of the quotient image is uniquely determined by a subset S subset of or equal to Vn and a class of switching equivalent sets A subset of or equal to En. We describe minimal vectors of all classes of image. We completely describe L-partition of six-dimensional space into Delaunay polytopes of the lattice L4 = √2 D6+.