On diffeomorphic mappings of one nondegenerate parallelepiped onto another

In this paper, we consider diffeomorphic mappings of a nondegenerate parallelepiped onto another such parallelepiped. We prove that the image of any face of the first parallelepiped under such a mapping is a certain face of the second parallelepiped. Moreover, we also obtain several auxiliary results on the transformation of boundary points of a nondegenerate parallelepiped under the action of a diffeomorphism.