A polyhedron is rigid if it cannot be continuously deformed into another configuration. A rigid polyhedron may have two or more stable
forms which cannot be continuously deformed into each other without bending or tearing
(Wells 1991).
A polyhedron that can change form from one stable configuration to another with only a slight transient nondestructive elastic stretch is called a multistable
polyhedron (Goldberg 1978).
A non-rigid polyhedron may be "shaky" (infinitesimally movable) or flexible. An
example of a concaveflexible polyhedron
with 18 triangular faces was given by Connelly (1978), and a flexible
polyhedron with only 14 triangular faces was subsequently found by Steffen (Mackenzie
1998).
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in Unsolved
Problems in Geometry. New York: Springer-Verlag, pp. 61-63, 1991.Cromwell,
P. R. "Equality, Rigidity, and Flexibility." Ch. 6 in Polyhedra.
New York: Cambridge University Press, pp. 219-247, 1997.Gluck,
H. Almost All Simply Connected Closed Surfaces are Rigid. Heidelberg, Germany:
Springer-Verlag, pp. 225-239, 1975.Goldberg, M. "Unstable
Polyhedral Structures." Math. Mag.51, 165-170, 1978.Graver,
J.; Servatius, B.; and Servatius, H. Combinatorial
Rigidity. Providence, RI: Amer. Math. Soc., 1993.Mackenzie,
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