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

Convex Polytopes, Dihedral Angles, Mean Curvature and Scalar Curvature