We describe all of 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.
Osamu Fujino. Sam Payne. "Smooth complete toric threefolds with no nontrivial nef line bundles." Proc. Japan Acad. Ser. A Math. Sci. 81 (10) 174 - 179, Dec. 2005. https://doi.org/10.3792/pjaa.81.174