  We classify the three-dimensional lattice polytopes with two interior lattice
points. Up to unimodular equivalence there are 22,673,449 such polytopes. This
classification allows us to verify, for this case only, a conjectural upper
bound for the volume of a lattice polytope with interior points, and provides
strong evidence for new conjectural inequalities on the coefficients of the
Ehrhart polynomial in dimension three.
