Abstract
This paper discusses the geometric properties and symmetries of general moiré patterns generated by homophase bilayers twisted by rotation 2δ. These patterns are generically quasiperiodic of rank 4 and result from the interferences between two basic periodicities incommensurate to each other, defined by the sites in the layers that are kept invariant through the symmetry operations of the structure. These invariant sites are distributed on the nodes of a set of lattices called Φ-lattices - where Φ runs on the rotation operations of the symmetry group of the monolayers - which are the centers of rotation 2δ + Φ transforming a lattice node of the first layer into a node of the second. It is demonstrated that when a coincidence lattice exists, it is the intersection of all the Φ-lattices of the structure.