2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/171459We study polytopes associated to factorisations of prime powers. These polytopes have explicit descriptions either in terms of their vertices or as intersections of closed halfspaces associated to their facets. We give formulae for their $f-$vectors.13 pagesCombinatorics52B05, 52B11, 52B20text