Abstract
We rigorously derive a theory of thin linearly quasicrystalline plates by studying the limit behavior of a three-dimensional flat body as its thickness tends to zero. We exhibit the existence of 26 different models, each of them linked to a specific set of boundary conditions. This stunning number of models is essentially the consequence of the coupling between displacements and a specific local rearrangement of matter at the microscopic scale that is called a phason. We exhibit the influence of the icosahedral order on the limit behavior.