Part III: Polyhedra c: Cauchy’s Rigidity Theorem. Joseph O’Rourke Smith College. Outline: Reconstruction of Convex Polyhedra. Cauchy to Sabitov (to an Open Problem) Cauchy’s Rigidity Theorem Aleksandrov’s Theorem Sabitov’s Algorithm. Reconstruction of Convex Polyhedra. graph
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Global rigidity == unique realization
Lemma: The total number of alternations in sign around the boundary of Q is ≥ 4.
(a) Zero sign alternations; (b) Two sign alts.
Lemma ≥ 4 V