Abstract: Cauchy proved that every convex polyhedron is rigid, in the sense that it cannot move preserving the shape of its faces. At the beginning of the XX century, Bricard discovered three families of flexible self-intersecting octahedra, and these are the only possible flexible ones. With the aid of the moduli space of stable rational curves, we attempt to re-prove the classical classification via a technique that may be applicable also to other situations. This is joint work with Georg Grasegger, Jan Legersky, and Josef Schicho.