Consider the complete bipartite graph $K_{3,3}$ in plane such that all its vertices lie on a circle. Is this framework locally rigid in plane (which I believe is the case) and if so, how to prove this?
I know that the above framework is not infinitesimally rigid. Moreover, it is known (due to Bolker and Roth, 1980) that the above framework becomes infinitesimally rigid if the vertices do not lie on a conic.
So if the answer to the question is yes, then this would be an example of a framework in general position that is locally rigid but not infinitesimally rigid. This specific question was also asked earlier in MathOverflow (https://mathoverflow.net/questions/453909/frameworks-in-general-position-that-are-locally-rigid-but-not-infinitesimally-ri ) ,but didn't receive any answer.