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The 23 Glazer tilt systems describing octahedral tilting in perovskites have been investigated. It is shown that in tilt systems a+a+a-, a+b+b-, a+a+c-, a+b+c-, a0b+b- and a0b+c- it is not possible to link together a three-dimensional network of perfectly rigid octahedra. In these tilt systems small distortions of the octahedra must occur. The magnitude of the distortions in the a+a+a- and a0b+b- tilt systems are estimated. A table of predicted space groups for ordered perovskites, A2MM'O6, for all 23 tilt systems is also given.
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