2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/132227We describe all of the smooth complete toric threefolds of Picard number 5 with no nontrivial nef line bundles, and show that no such examples exist with Picard number less than 5.8 pages. This is an improved version of the second author's preprint math.AG/0501204 v2: minor revisions. To appear in Proc. Japan Acad. Ser. AAlgebraic Geometry14M25; 14C20text