The Gram-Sommerville and Gauss-Bonnet theorems and combinatorial geometric measures for noncompact polyhedra (Q1188447)

For the case of noncompact and unbounded polyhedra \(P\) in a finite- dimensional affine space over an ordered field, there are introduced the tangential curvature function, tangential curvature, normal curvature function, and Gaussian curvature of \(P\) near a face and infinity. With these functions classical Gram-Sommerville and Gauss-Bonnet theorems are generalized. Also higher-dimensional geometric measures on the space of polyhedra are studied.