  It is known that the sectional genus of a polarized variety has an upper
bound, which is an extension of the Castelnuovo bound on the genus of a
projective curve. Polarized varieties whose sectional genus achieves this bound
are called Castelnuovo. On the other hand, a lattice polytope is called
Castelnuovo if the associated polarized toric variety is Castelnuovo. Kawaguchi
characterized Castelnuovo polytopes having interior lattice points in terms of
their $h^*$-vectors. In this paper, as a generalization of this result, a
characterization of all Castelnuovo polytopes will be presented. Finally, as an
application of our characterization, we give a sufficient criterion for a
lattice polytope to be IDP.
