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15.8: Combining symmetry

  • Page ID
    31578
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    Only certain combinations of symmetry operation can exist in a crystal structure. This is because one symmetry element operating on another will generate a third symmetry element in the structure and this can end up generating an infinite number of symmetry elements, as shown in the animation below:

    In fact, there are only 32 permitted combinations of mirror planes, rotation axes, centres of symmetry and inversion axes. These are known as the 32 point groups. Each point group is a finite set of mutually compatible symmetry elements. When the symmetry elements of a point group are operated on each other, they simply generate one of the other elements within the group.


    This page titled 15.8: Combining symmetry is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by Dissemination of IT for the Promotion of Materials Science (DoITPoMS).

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