  Let $\lambda$ be a dominant weight of a finite dimensional simple Lie algebra
and $W$ the Weyl group. The convex hull of $W\lambda$ is defined as the weight
polytope of $\lambda$. We provide a new proof that there is a natural bijection
between the set of orbits of the nonempty faces of the weight polytope under
the action of the Weyl group and the set of the connected subdiagrams of the
extended Dynkin diagram that contain the extended node $\{-\lambda\}$. We show
that each face of the polytope can be transformed to a standard parabolic face.
We also show that a standard parabolic face is the convex hull of the orbit of
a parabolic subgroup of $W$ acting on the dominant weight. In addition, we find
that the linear space spanned by a face is in fact spanned by roots.
