Example 10 Find the total number of symmetry elements that exist in a cube.
Solution: Looking at Fig. 6.13, we find that there exist:
(i) 2-fold axes parallel to the face diagonal and passing through the center of the
cube. There are six such axes.
(ii) 3-fold axes passing through the body diagonal. There are four such axes.
(iii) 4-fold symmetry about an axis passing through the center of two opposite
faces. There are three such symmetry axes.
Fig. 6.13 Representation of different symmetries of a cube
6.1 Unit Cell Symmetry Elements/Operations
217
Solution: Looking at Fig. 6.13, we find that there exist:
(i) 2-fold axes parallel to the face diagonal and passing through the center of the
cube. There are six such axes.
(ii) 3-fold axes passing through the body diagonal. There are four such axes.
(iii) 4-fold symmetry about an axis passing through the center of two opposite
faces. There are three such symmetry axes.
Fig. 6.13 Representation of different symmetries of a cube
6.1 Unit Cell Symmetry Elements/Operations
217