Delaunay polytopes of cut lattices

We continue 3], the study of the lattice L n generated by cuts of the complete graph on a set V n of n vertices. The lattice L n spans an N = ? n 2-dimensional space of all functions deened on a set V 2 n of all unordered pairs of the set V n. We prove that the cut polytope, i.e. the convex hull of all cuts, is an asymmetric Delaunay polytope of L n. Symmetric Delaunay polytopes of a lattice L are completely described by classes of the quotient 1 2 L=L. We show that a class of the quotient 1 2 L n =L n is uniquely determined by a subset S V n and a class of switching equivalent sets A V 2 n. We describe minimal vectors of all classes of 1 2 L n =L n. We completely describe L-partition of 6-dimensional space into Delaunay polytopes of the lattice L 4 = p 2D +2 6 .