Although the rigidity theorem states that if the faces of a convex polyhedron are made of metal plates and the polyhedron edges are replaced by hinges, the polyhedron would be rigid, concave polyhedra need not be rigid. A nonrigid polyhedron may be "shaky" (infinitesimally movable) or flexible (continuously movable; Wells 1991).
In 1897, Bricard constructed several self-intersecting flexible octahedra (Cromwell 1997, p. 239). Connelly (1978) found the first example of a true flexible polyhedron, consisting of 18 triangular faces (Cromwell 1997, pp. 242-244). Mason discovered a 34-sided flexible polyhedron constructed by erecting a pyramid on each face of a cube adjoined square antiprism (Cromwell 1997). Kuiper and Deligne modified Connelly's polyhedron to create a flexible polyhedron having 18 faces and 11 vertices (Cromwell 1997, p. 245), and Steffen found a flexible polyhedron with only 14 triangular faces and 9 vertices (shown above; Cromwell 1997, pp. 244-247; Mackenzie 1998). Maksimov (1995) proved that Steffen's is the simplest possible flexible polyhedron composed of only triangles (Cromwell 1997, p. 245).
Connelly et al. (1997) proved that a flexible polyhedron must keep its volume constant, confirming the so-called bellows conjecture (Mackenzie 1998).
