  We derive upper and lower bounds on the gradients of Wachspress coordinates
defined over any simple convex d-dimensional polytope P. The bounds are in
terms of a single geometric quantity h_*, which denotes the minimum distance
between a vertex of P and any hyperplane containing a non-incident face. We
prove that the upper bound is sharp for d=2 and analyze the bounds in the
special cases of hypercubes and simplices. Additionally, we provide an
implementation of the Wachspress coordinates on convex polyhedra using Matlab
and employ them in a 3D finite element solution of the Poisson equation on a
non-trivial polyhedral mesh. As expected from the upper bound derivation, the
H^1-norm of the error in the method converges at a linear rate with respect to
the size of the mesh elements.
