Convex Polytopes, Dihedral Angles, Mean Curvature and Scalar Curvature

We approximate boundaries of convex polytopes by smooth hypersurfaces $Y=Y_{\epsilon }$ with {\it positive mean curvatures} and, by using basic geometric relations between the scalar curvatures of Riemannin manifolds and the mean curvatures of their boundaries, establish {\it lower bound on the dihedral angles} of these polytopes.