Cones of partial metrics

A partial semimetric on a set X is a function (x,y)↦p(x,y)∈≥0 satisfying p(x,y)=p(y,x), p(x,y)≥p(x,x) and p(x,z)≤p(x,y)+p(y,z)−p(y,y) for all x,y,z∈X. We study here the polyhedral convex cone PSMETn of all partial semimetrics on n points, using computations done for n≤6. We present data on those cones and their relatives: the number of facets, of extreme rays, of their orbits, incidences, characterize 0,1- valued extreme rays, etc.