Principles of the structural design of photonic quasicrystals

A theory of the structure of icosahedral quasicrystals is being developed based on the tiling theory and the concept of unit cells. An algorithm is proposed that includes filling several types of unit cells with atoms according to the local matching rules and filling the space with unit cells through inflations and deflations. The theory makes it possible to design the structures of icosahedral quasicrystals of all the three types within both groups of icosahedral symmetry, including the right-handed and left-handed enantiomorphic forms.