Newton polygons as lattice points

Let M be the reduction modulo p of a Shimura variety, and let N(M) be the partially ordered set predicted to be the set of all types occurring in the stratification of M by Newton polygons, in the context of F-isocrystals with additional structures. We prove that N(M) is ranked (or catenary), in the sense that any two maximal chains have the same length. We also give a Lie-theoretic formula for the distance between two comparable elements in N(M). This formula can be used to give the expected dimension of the Newton strata of M.