Symmetry element

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A symmetry element is a lattice element about which a symmetry operation is performed. Symmetry elements are classified on the basis of the dimensionality N of the space on which they act, the upper limit on the dimensionality of the symmetry element being N-1.

One-dimensional space

The only symmetry element that exists in this space is the reflection point (mirror point).

Two-dimensional space

In this space, two types of symmetry elements exist: zero and one-dimensional:

  • rotations points
  • reflection lines (mirror lines)

The inversion centre does not exist in spaces of even number of dimensions.

Three-dimensional space

In this space, three types of symmetry elements exist: zero, one- and two-dimensional:

  • inversion centres
  • rotations axes
  • reflection planes (mirror planes)