# Frameworks in general position that are locally rigid but not infinitesimally rigid

The classical theorem of Asimow and Roth says that for a generic framework (i.e., coordinates of the nodes are algebraically independent), local rigidity and infinitesimal rigidity are equivalent. I was wondering how this theorem fails if we replace "generic'' by "(affine) general position". So my question is: What are examples of frameworks whose nodes are in general position and locally rigid but not infinitesimally rigid?

• See Constructive approaches to the rigidity of frameworks (theses.hal.science/tel-00992387). In page 39, image 3.2.c they give an example of a framework that is locally but not infinitesimally rigid, without 3 points being colinear. Sep 26, 2023 at 6:15
• It further mentions a theorem of Asimow and Roth (th 3.2.3) that says generic framework is locally rigid if and only if it is infinitesimally rigid Sep 26, 2023 at 7:15
• @caduk Thanks for the reference and the example. But it does not give any argument (which is what I am interested in) to show that it is actually rigid. Sep 26, 2023 at 11:15