N. H. Kuiper has generalized the notion of total absolute curvature for compact polyhedra in euclidean space by considering the critical points of all height functions (cf. [12]). On the other hand in the case of compact smooth manifolds with boundary in En there is a certain relation between the total absolute curvatures of the total space, the interior and the boundary (cf. [9]). In this note we show an analogous relation in the case of compact polyhedral manifolds with boundary leading to theorems of the Chern/Lashof type (cf. [3], [7]).