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.
Rigidity Theorem
See also
Flexible Polyhedron, Rigid Polyhedron, Shaky PolyhedronExplore with Wolfram|Alpha
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.Referenced on Wolfram|Alpha
Rigidity TheoremCite this as:
Weisstein, Eric W. "Rigidity Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RigidityTheorem.html