Possible rotational symmetries of a lattice ↩

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created: 2021-10-31 18:15:54
modified: 2022-01-10 04:13:04

Let's consider a 2D lattice. This lattice's rotational symmetry cannot be arbitrary due to its discrete translational symmetry.

Look at the rotation by the angle . This operation applied to lattice vector results in another lattice vector and its inverse as well .

Then is a lattice vector as well and it is parallel to , so:

The only possible solutions to this are:

This means that only rotations are possible where .

The possible structures are these: