On toroidal embeddings of 3-folds

Using combinatorial methods, we classify all birational morphisms blowing m ≦ 5 divisors down to a point. Those which do not factor through the blowing up of a point are treated in the body of the paper, and the factorizable morphisms are computed in an appendix. The relevance of this classification to the determination of the nature of the "general" toric morphism is discussed.