  We study certain faces of the normal polytope introduced by Feigin,
Littelmann and the author whose lattice points parametrize a monomial basis of
the PBW-degenerated of simple modules for $\mathfrak{sl}_{n+1}$. We show that
lattice points in these faces parametrize monomial bases of PBW-degenerated
Demazure modules associated to Weyl group elements satisfying a certain closure
property, for example Kempf elements. These faces are again normal polytopes
and their Minkowski sum is compatible with tensor products, which implies that
we obtain flat degenerations of the corresponding Schubert varieties to PBW
degenerated and toric varieties.
