2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59298We introduce polyhedral cones associated with $m$-hemimetrics on $n$ points, and, in particular, with $m$-hemimetrics coming from partitions of an $n$-set into $m+1$ blocks. We compute generators and facets of the cones for small values of $m,n$ and study their skeleton graphs.19 pages. To appear in Discrete MathematicsCombinatoricstext