2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/209427In this paper we study geodesic Ptolemy metric spaces $X$ which allow proper and cocompact isometric actions of crystallographic or, more generally, virtual polycyclic groups. We show that $X$ is equivariantly rough isometric to a Euclidean space.20 pages, 1 figureMetric Geometry53C20; 53C24text