Toric Fano three-folds with terminal singularities

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 be smooth) and 401 toric Fano 3-folds with terminal singularities that are not Q-factorial.