The minimum number of basis vectors is the rank of the vector module. If the rank n is larger than the space dimension, the structure is not periodic, but aperiodic. There are four classes of aperiodic structures, but these classes have an overlap:.
Online Dictionary of Crystallography. Applications There are four classes of aperiodic structures, but these classes have an overlap: incommensurately modulated crystal phases See incommensurate modulated crystal phases , incommensurate composite structures See incommensurate composites , quasicrystals see quasicrystals , and incommensurate magnetic structures See incommensurate magnetic structures.
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