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More recently, Glazer developed a very influential notation for describing the 23
different tilt systems that have been observed (Glazer, 1972). The description is based
on the rotations of the octahedra about each of the three Cartesian axes. The direction
of the rotation about any one axis, relative to the rotations about the other two axes, is
specified by a letter with a superscript that indicates whether the rotations in adjacent
layers, which are coupled to the other layers via the vertex-sharing octahedra, are in
the same (+) or opposite (¡ª) directions. For example, a+a+a+ signifies an equivalent
rotation about the three axes in each of the adjacent layers. Similarly, in the a0a0c+ tilt
system, the octahedra are rotated only about the axes parallel to the z axis, with the
same direction in both layers.
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