Space-Group Symmetries


Up to this point, structures of mostly finite objects have been discussed. Thus, point groups were applicable. A simplified compilation of various symmetries was presented in Figure 2-41 and Table 2-2. The point-group symmetries are characterized by the lack of periodicity in any direction. Periodicity may be introduced by translational symmetry. If periodicity is present, space groups are applicable for the symmetry description. There is a slight inconsistency here in the terminology. Even a three-dimensional object may have point-group symmetry. On the other hand, the so-called dimensionality of the space group is not determined by the dimensionality of the object. Rather, it is determined by its periodicity. The following groups are space-group symmetries, where the superscript refers to the dimensionality of the object and the subscript to the periodicity.


Symmetry Element Symmetry Class Screw Axis Translation Axis Photograph Courtesy 
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© Plenum Press 1995

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