FFLV polytopes are string polytopes

In this paper, we establish that FFLV polytopes, which describe monomial bases compatible with the PBW filtration on finite-dimensional simple modules for $\text{lie}{sl}_n$ and $\text{lie}{sp}_n$, are actually string polytopes as described by Littelmann and Berenstein-Zelevinsky for Demazure modules of higher-rank Lie algebras.