2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/149846We prove the following main result: Let X be a Fano 3-fold with terminal Q-factorial singularities and X does not have a small extremal ray and a face of Kodaira dimension 1 or 2 for Mori polyhedron of X. Then the Picard number ρ(X) < 8.35 pages, AMS-Tex, version 2.1, Preprint MSRI Berkeley, June 057-93 (corrected variant)Algebraic Geometrytext