Space-groups symmetries spirals

There are some crystal structures in which further symmetries are present in addition to those prescribed by their three-dimensional space groups. The phenomenon is called hypersymmetry [102], Thus, it refers to symmetry features not included in the system of the 230 three-dimensional space groups. For example, phenol molecules, connected by hydrogen bonds, form spirals with threefold screw axes as indicated in Figure 9-55. This screw axis does not extend, however, to the whole crystal, and it does not occur in the three-dimensional space group characterizing the phenol crystal. 

Figure 9-55. The molecules in the phenol crystal are connected by hydrogen bonds and are forming spirals with a threefold screw axis. This symmetry element is not part of the three-dimensional space group of the phenol crystal. After Zorky and Koptsik [103],...

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