Is there an analogue of Poincare-Hopf theorem for polytopes?

I want to apply it in the following situation. I have a polytope in $R^n$ and a smooth explicitly given vector field in $R^n$. I want to find the number of points where the field is normal to the surface of the polytope (rather, lies in the normal cone). If the polytope was a smooth compact manifold, I'd project the field to the tangent space and apply Poincare-Hopf theorem. Is there a version of Poincare-Hopf theorem which lets me do something similar for polytopes?