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Rigidity Theorem

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).

See also Flexible Polyhedron, Rigid


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 Eric W. Weisstein