The transition from the crystalline to quasicrystalline phase in the Al65Cu20Co15 alloy was observed and interpreted based on a structure defect model. The structures of the approximants are basically periodic but highly microtwinned. The transition to the quasicrystalline state upon annealing is a result of the increased appearance of microtwinned regions in the structures, driven by an inherent strain present in their structures. The ideas of twinning and tiling, formerly two entirely different schools of thought on the structure of the quasicrystals, appear to be closely related in the proposed structural description of this transition.