In this talk I consider 3D rod-and-pinion frameworks constructed from 3D quasicrystal structures and ask how can we make such structures rigid by introducing plates in the faces of the rhombohedra. Although this question remains open, we will overview related results and possible approaches using rigidity results for quasicrystal frameworks in 2D and cubical frameworks in 3D.Title: Rigidity of quasicrystals in 3D