  In this paper, we study nearly Gorensteinness of Ehrhart rings arising from
lattice polytopes. We give necessary conditions and sufficient conditions on
lattice polytopes for their Ehrhart rings to be nearly Gorenstein. Using this,
we give an efficient method for constructing nearly Gorenstein polytopes.
Moreover, we determine the structure of nearly Gorenstein (0, 1)-polytopes and
characterise nearly Gorensteinness of edge polytopes and graphic matroids.
