2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60159The purpose of this article is to give a proof of the Orbifold Theorem announced by Thurston in late 1981: If $O$ is a compact, connected, orientable, irreducible and topologically atoroidal 3-orbifold with non-empty ramification locus, then $O$ is geometric. As a corollary, any smooth orientation preserving non-free finite group action on $S^3$ is conjugate to an orthogonal action.Revised version (one single paper instead of the previous 2)Geometric Topology57M50text