Discrete Geometry and Combinatorics Seminar
Cauchy's Rigidity theorem states that a convex polyhedron is uniquely determined by its combinatorial type and face lattices. Various results related to the rigidity of polyhedra have been proved by Dehn, Whiteley, Alexandrov, Connelly and many others. In this talk, we discuss the rigidity of a polyhedron with only the combinatorial type and edge lengths as constraints. The question of the regular dodecahedron was specifically raised by Martin Winter at Fields Institute this July. A solution to his problem will be given in the talk. Then we discuss some of the open problems and conjectures about this type of rigidity.