Symmetry element

In chemistry and crystallography, a symmetry element is a point, line, or plane about which symmetry operations can take place. In particular, a symmetry element can be a mirror plane, an axis of rotation (either proper and improper), or a center of inversion.[1][2][3] For an object such as a molecule or a crystal, a symmetry element corresponds to a set of symmetry operations, which are the rigid transformations employing the symmetry element that leave the object unchanged. The set containing these operations form one of the symmetry groups of the object. The elements of this symmetry group should not be confused with the "symmetry element" itself. Loosely, a symmetry element is the geometric set of fixed points of a symmetry operation. For example, for rotation about an axis, the points on the axis do not move and in a reflection the points that remain unchanged make up a plane of symmetry.

  1. ^ Robert G. Mortimer (10 June 2005). Mathematics for Physical Chemistry. Academic Press. pp. 276–. ISBN 978-0-08-049288-9.
  2. ^ "Symmetry element". Online Dictionary of Crystallography. 2021-09-25. Retrieved 2021-09-25.
  3. ^ Wolff, P.M. de; et al. (1989). "Definition of symmetry elements in space groups and point groups. Report of the International Union of Crystallography Ad-Hoc Committee on the Nomenclature of Symmetry". Acta Crystallographica Section A. 45 (7): 494–499. doi:10.1107/S0108767389002230. ISSN 0108-7673. Retrieved 2021-09-29.