Electron microscopy
Rotation Axis (1, 2, 3, 4 and 6 (Cn)) in Crystallography
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In reality, not all rotational symmetries are allowed in crystals. The only rotational symmetries possible in crystal lattices are 2, 3, 4 and 6, because it is impossible to fill space with other symmetries (e.g. 5, 7 …). However, this restriction does not apply to molecular symmetry, for instance, C-reactive protein has 5-fold rotational symmetry, GroEL has 7-fold, etc. On the other hand, quasi-crystals, e.g. with 5-fold rotational symmetry, can be formed.

2-, (b) 3-, (c) 4- and (d) 6-rotational symmetries 3 fold symmetry 4 fold symmetry 6 fold symmetry

Figure 1622. (a) 2-, (b) 3-, (c) 4- and (d) 6-rotational symmetries.

As an example, the three space groups C2/m, C2 and Cm have the same systematic forbidden reflections which are caused by the C-centering (h+k = 2n+1). The other symmetry operations in the three space groups, e.g. 2-fold rotation axis (2) and mirror plane (m) in the C2/m space group, do not cause forbidden reflections.

Rotation axes are observed directly with ZOLZ and HOLZ lines in CBED patterns when the beam is aligned with the rotation axis.