Flexibility of frameworks consisting of parallelograms and triangles

Abstract

A well known result of Bolker and Crapo determines how to make a grid of squares rigid by bracing, i.e., adding diagonals. The result had been generalized to bracing frameworks consisting of parallelograms with richer combinatorial structure. In this talk we focus on frameworks that besides (braced) parallelograms contain also triangles that do not originate from bracing. We define a certain equivalence on the edge set of the graph to show that such a framework is flexible if and only if it is infinitesimally flexible if and only if it has at least two equivalence classes.