Cauchy proved that convex polyhedra are rigid. Dehn later proved that they are also infinitesimally rigid. We are interested in a conjectured generalization: a polyhedron P with vertices in convex position which is decomposable (it can be cut into convex pieces without adding any interior vertex) is infinitesimally rigid. This is true under the (weak) additional condition that P is codecomposable (its complement in its convex hull is decomposable), for instance if P is star-shaped with respect to one of its vertices. (Joint with Ivan Izmestiev.)