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created: 2021-10-31 18:29:04
modified: 2022-01-10 04:13:04
A crystal lattice can have other symmetries, not just the discrete translational symmetry. These transformations can be rotation, mirroring or a combination of these (roto-reflection), etc. These transformations have a fix point so we call them point transformations.
The group that contains all the symmetries of the crystal is called the space group. It contains the combinations of the applicable point groups and the crystal's translational symmetry.
A crystal's lattice can only have 2, 3, 4 or 6-fold rotational symmetries.
Neumann's principle tells us that a crystal's symmetries manifest themselves as symmetries in its physical properties as well.