Molecular Point Groups

The symmetry elements and operations characterizing the geometry of a molecule form a point group. The possible symmetry elements are: the identity element, -fold axis of symmetry, plane of symmetry, center of inversion, and -fold rotation-reflection axis.
This Demonstration illustrates the symmetry elements for 34 point groups (including two limiting groups) and a ball-and-stick model for a corresponding molecule. The symbols for the symmetry elements and more example molecule names are listed.

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Mathematicians developed abstract group theory in the early century. In the 1920s and 1930s the theory of molecular symmetry was applied to atoms, molecules, and crystals. The Hermann–Mauguin notation is most often used to describe the symmetries in crystals, while for molecules and their spectroscopic properties the Schönflies notation is preferred.
Use the "type of view" radio button to show a ball-and-stick figure of a molecule with the same molecular point group. In molecular view, the checkboxes "show symmetry planes" and "show symmentry axes" are enabled. Chemical names for further examples are listed, if available.
ChemSpider and CSD are the sources for the ball and stick figures. The ChemSpider IDs and CCDC refcodes for each used structure are listed in the Demonstration.
References
[1] M. Hargittai and I. Hargittai, Symmetry through the Eyes of a Chemist, New York: Springer, 2009.
[2] U. Müller, Inorganic Structural Chemistry, New York: J. Wiley & Sons, 2006.
[3] G. Miessler and D. Tarr, Inorganic Chemistry, NJ: Prentice-Hall, 2004.
[4] G. Lawrance, Introduction To Coordination Chemistry, New York: J. Wiley & Sons, 2010.
[5] M. Hollas, Modern Spectroscopy, New York: J. Wiley & Sons, 2004.
[6] D. Johnston. "Gallery." Symmetry @ Otterbein. (May 2012) symmetry.otterbein.edu/gallery/index.html.
[7] S. Immel. "Molecular Structures of Organic Compounds - Symmetry and Point Groups." Technische Universitat Darmstadt. (May 2012) csi.chemie.tu-darmstadt.de/ak/immel/tutorials/symmetry/index.html.
[8] Wikipedia. "Punktgruppen in der Molekülphysik." (May 2012) de.wikipedia.org/wiki/Punktgruppe# Punktgruppen_in _der _Molek.C3.BClphysik.
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