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A group-theoretical analysis is made of the structures derived from the aristotype cubic perovskite (Pm3m) by the simple tilting of rigid octahedral units. The tilting is mediated by the irreducible representations R^+_4 and M^+_3 or the two in combination. These result in 15 possible structures, compared with the 23 possibilities suggested previously by Glazer [Acta Cryst. (1972), B28, 3384-3392]. The analysis makes the group-subgroup relationships apparent.
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