Consider a closed finite triangulated oriented polyhedral surface S in three-space. Regard the edges of S as rigid inextendible incompressible bars at ideal universal joints, the vertices of S. There are several examples when the bar constraints on the edges allow the shape of S to change. In other words S has a non-trivial flex. We show that the volume bounded by S during such a flex is constant. This can be though of as saying that there is no exact mathematical "bellows" that can change its enclosed volume. This result (as well the notion of bounding volume) can be generalized considerably to consider the case when S is any (possibly) singular oriented simplicial cycle of dimension n-1 in any Euclidean space of dimension n, where n is three or greater. This is joint work with I. Sabitov and A. Walz.