| 单词 | Rigidity Theorem |
| 释义 | Rigidity TheoremIf the faces of a convex Polyhedron were made of metal plates and the Edges werereplaced by hinges, the Polyhedron would be Rigid. The theorem was stated by Cauchy (1813), although amistake 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 triangularfaces 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. |
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