Cut Lattices and Equiangular Lines

The cut polytopePCutnis an L-polytope of the latticeLn,affinely generated by its vertices. We consider cut-sublattices ofLngenerated by subsets of cuts. Ifnis even,Lnis generated by an odd system. We give a description of sets of equiangular lines related toLnand define a sequence of symmetric 2-designs related to these equiangular lines. The first 4 designs of this sequence are known to exist.