Rotation about an -fold axis of symmetry

The symmetry operation of rotation about an -fold axis (the symmetry element) is denoted by the symbol C , in 

If a molecule possesses more than one type of n-axis, the axis of highest value of n is called the principal axis it is the axis of highest molecular symmetry. For example, in BF3, the C3 axis is the principal axis. 

In some molecules, rotation axes of lower orders than the principal axis may be coincident with the principal axis. For 

Among the following, why does only XeF4 contain a 4-fold principal rotation axis CF4, SF4, [BF4] and XeF4  

3 or 4. Applying this notation to the BF3 molecule in Fig. 3.1 gives a value of = 3 (eq. 3.1), and therefore we say that the BF3 molecule contains a C3 rotation axis. In this case, the axis lies perpendicular to the plane containing the molecule. 

In addition, BF3 also contains three 2-fold (C2) rotation axes, each coincident with a B—F bond as shown in Fig. 3.2. 

In some molecules, rotation axes of lower orders than the principal axis may be coincident with the principal axis. For example, in square planar XeF4, the principal axis is a C4 axis but this also coincides with a C2 axis (see Fig. 3.4). 

The symmetry operation of rotation about an n-fold axis 

Where a molecule contains more than one type of C axis with the same value of n, they are distinguished by using 

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