Abstract Beck et al. characterized the grid graphs whose perfect matching polytopes are Gorenstein and they also showed that for some parameters, perfect matching poly- topes of torus graphs are Gorenstein. In this paper, we complement their result, that is, we characterize the torus graphs whose perfect matching polytopes are Gorenstein. Beck et al. also gave a method to construct an infinite family of Goren- stein polytopes. In this paper, we introduce a new class of polytopes obtained from graphs and we extend their method to construct many more Gorenstein polytopes.
