A classification of smooth convex 3-polytopes with at most 16 lattice points

We provide a complete classification up to isomorphism of all smooth convex lattice 3-polytopes with at most 16 lattice points. There exist in total 103 different polytopes meeting these criteria. Of these, 99 are strict Cayley polytopes and the remaining four are obtained as inverse stellar subdivisions of such polytopes. We derive a classification, up to isomorphism, of all smooth embeddings of toric threefolds in ℙN where N≤15. Again we have in total 103 such embeddings. Of these, 99 are projective bundles embedded in ℙN and the remaining four are blow-ups of such toric threefolds.