Rotatory-reflection Sn

Another operation that yields an image which is identical to the original is a combination of rotation and reflection. The body is turned by 360°/n about an axis and then submitted to reflection on a plane perpendicular to the axis. With the same result, the reflection can be performed first and the rotation second. This symmetry operation is called a rotatory-reflection and the symmetry element is an n-fold rotatory-reflection axis. The symbol Sn denotes the symmetry operation as well as the symmetry element. Neither the involved axis nor the plane need to be symmetry elements for themselves. The values for n in rotatory-reflection Sn are even numbers or 1.
Rotatory-reflection axes Sn with n = 1, 2 and 6.
- For S1 we have the special case of an ordinary reflection on a horizontal plane and
- S2 equals inversion i.

Example 1: Rotatory-reflection S4 of the molecule CH4 (Movie, 1.2 MByte)

Example 2: SiF4

SiF4 possesses four axes C3 . There is no axis C4 but a rotatory-reflection axis S4.

Example 3: trans-1,2 Dichlorethen


If the molecule trans-1,2 Dichlorethen is turned about 180° around the CC-σ-bond and subsequently reflected, a rotary-reflection is performed. The axis S2 runs through both carbon atoms. As mentioned above, the symmetry elements S2i and σ ≡ S1.


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