  We prove that for every complex classical group $G$ the string polytope
associated to a special reduced decomposition and any dominant integral weight
$\lambda$ will be a lattice polytope if and only if the highest weight
representation of the Lie algebra of $G$ with highest weight $\lambda$
integrates to a representation of $G$ itself. This affirms an earlier
conjecture and shows that every partial flag variety of a complex classical
group admits a flat projective degeneration to a Gorenstein Fano toric variety.
