Abstract.
Aleksandrov [1] proved that a simple convex d -dimensional polytope, d ≥ 3 , is infinitesimally rigid if the volumes of its facets satisfy a certain assumption of stationarity. We extend this result by proving that this assumption can be replaced by a stationarity assumption on the k -dimensional volumes of the polytope's k -dimensional faces, where k ∈{1,. . .,d-1} .
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Received November 20, 1997.
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Bauer, C. Infinitesimal Rigidity of Convex Polytopes . Discrete Comput Geom 22, 177–192 (1999). https://doi.org/10.1007/PL00009453
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DOI: https://doi.org/10.1007/PL00009453