2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62404This note shows that a certain toric quotient of the quintic Calabi-Yau threefold in projective four-space provides a counterexample to a recent conjecture of Cox and Katz concerning nef cones of toric hypersurfaces.Originally written in 1999. To appear in Math.ZAlgebraic Geometry14J32, 14C34, 14M25text