  This paper concerns the characterisation of second order marginals for random
sets in a discrete setting. Under the instance of unit covariances, this
problem possesses a combinatorial symmetry, exploited jointly in the companion
paper to give a heuristic procedure to check realisability. In particular we
disprove Matheron's conjecture, and explicit partially the structure of the
convex body formed by realisable unit covariances in a finite set.
