This paper classifies all toric Fano $3$-folds with terminal singularities. This is achieved by solving the equivalent combinatorial problem; that of finding, up to the action of $GL(3,\Z)$, all convex polytopes in $\Z^3$ which contain the origin as the only non-vertex lattice point. We obtain, up to isomorphism, $233$ toric Fano $3$-folds possessing at worst $\Q$-factorial singularities (of which $18$ are known to besmooth) and $401$ toric Fano $3$-folds with terminal singularities that are not $\Q$-factorial.
"Toric Fano three-folds with terminal singularities." Tohoku Math. J. (2) 58 (1) 101 - 121, 2006. https://doi.org/10.2748/tmj/1145390208