  We prove a generalization of a result by Dong and Santos-Sturmfels about the
homotopy type of the Alexander dual of balls and spheres. Our results involve
NH-manifolds, which were recently introduced as the non-homogeneous (or
non-pure) counterpart of classical polyhedral manifolds. We show that the
Alexander dual of an NH-ball is contractible and the Alexander dual of an
NH-sphere is homotopy equivalent to a sphere. We also prove that NH-balls and
NH-spheres arise naturally as the double duals of standard balls and spheres.
