The bellows conjecture asserts that all flexible polyhedra keep a constant volume as they are flexed (Cromwell 1997). The conjecture was apparently proposed by Dennis Sullivan, although Sullivan may not be the actual originator (R. Connelly, pers. comm., Feb. 17, 2007). This conjecture was proven by Connelly et al. (1997).
Bellows Conjecture
See also
Flexible PolyhedronExplore with Wolfram|Alpha
References
Connelly, R.; Sabitov, I.; and Walz, A. "The Bellows Conjecture." Contrib. Algebra Geom. 38, 1-10, 1997.Cromwell, P. R. Polyhedra. New York: Cambridge University Press, pp. 245 and 247, 1997.Mackenzie, D. "Polyhedra Can Bend But Not Breathe." Science 279, 1637, 1998.Cite this as:
Weisstein, Eric W. "Bellows Conjecture." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BellowsConjecture.html