As discussed in the introduction, our result immediately implies that any connected triangulated closed polyhedral surface is generically 3 rigid. Whether or not the surface can be embedded in R is irrelevant to our theorem. Corollary. Thus we have the following corollary. 1- manifold is generically 3- rigid. The 1-skeleton of any abstract triangulation of a Here are two applications of this corollary. In Chapter 1 we introduced as quickly as possible the definition of generic rigidity, which is all that is necessary to prove the result. But there is another type of rigidity for frameworks that is related to the rigidity that we have discussed and which is important in its own right, namely static rigidity
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