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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 
and 
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.
and 
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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