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A group-theoretical analysis is made of the structures derived from the aristotype cubic perovskite (Pm 3¯ m) 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), B 28, 3384–3392. The analysis makes the group–subgroup relationships apparent.
Howard et al. (1998) studied this question.