If the faces of a *convex* Polyhedron were made of metal plates and the Edges were
replaced by hinges, the Polyhedron would be Rigid. The theorem was stated by Cauchy (1813), although a
mistake in this paper went unnoticed for more than 50 years. An example of a *concave* ``Flexible Polyhedron''
(with 18 triangular faces) for which this is not true was given by Connelly (1978), and a Flexible Polyhedron with only 14 triangular
faces was subsequently found by Steffen (Mackenzie 1998).

**References**

Cauchy, A. L. ``Sur les polygones et les polyèdres.'' *XVIe Cahier* **IX**, 87-89, 1813.

Connelly, R. ``A Flexible Sphere.'' *Math. Intel.* **1**, 130-131, 1978.

Graver, J.; Servatius, B.; and Servatius, H. *Combinatorial Rigidity.* Providence, RI: Amer. Math. Soc., 1993.

Mackenzie, D. ``Polyhedra Can Bend But Not Breathe.'' *Science* **279**, 1637, 1998.

© 1996-9

1999-05-25