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If the faces of a convex polyhedron were made of metal plates and the polyhedron 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.
 Flexible Polyhedron, Rigid Polyhedron, Shaky Polyhedron
References
Cauchy, A. L. "Sur les polygons et le polyhéders." XVIe Cahier IX, 87-89, 1813.
Cromwell, P. R. "Cauchy's Rigidity Theorem." In Polyhedra. New York: Cambridge University Press, pp. 228-233, 1997.
Dehn, M. "Über die Strakheit knovexer Polyeder." Math. Ann. 77, 466-473, 1916.
Goldberg, M. "Unstable Polyhedral Structures." Math. Mag. 51, 165-170, 1978.
Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, pp. 161-162, 1991.
Eric W. Weisstein
© 1999 CRC Press LLC,
© 1999-2003 Wolfram Research, Inc.
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