Rigidty of quasicrystal rod-and-pinion frameworks in 2D and 3D

Deciding wether a 2D rod-and-pinion framework is rigid can be done by checking that its underlying graph satisfies the Laman conditions. For frameworks with a special configuration such as grids of squares, there is a simpler way to associate a graph to the framework and decide if it is rigid or not. In this talk I will consider frameworks that come from Penrose tilings and show that we can decide the rigidity of these graphs as we do for grids of squares. There is no generalization of Laman conditions for rigidity of 3D graphs but perhaps we can prove a generalization of 2D results for cubical frameworks. Pictures and real time interactive animations will be present throughout this talk to illustrate important concepts.