A matricial theory of coincidence-site and displacement-shift-complete (DSC) lattices of arbitrary dimension is developed. Vector bases for these lattices can easily be determined from particular factorizations of the matrix defining the relative orientation. Various properties of the two lattices are derived, including the reciprocity relations. The general conditions for coincidence and the problem of coincidence in sublattices of lower dimension are also discussed.
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M. Amaral Fortes (1983) studied this question.
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