Symmetricaly Equivalent Orientations edit page

A crystal orientation always appears as a class of symmetrically equivalent rotations which all transform the crystal reference frame into the specimen reference frame and are physicaly not distinguishable.

Lets start by defining some random orientation

Since orientations transform crystal coordinates into specimen coordinates crystal symmetries will act from the right and specimen symmetries from the left

We observe that only the third Euler angle phi2 changes as this Euler angle applies first to the crystal coordinates.

Combining crystal and specimen symmetry we obtain 6 crystallographically equivalent orientations to ori

A shortcut for this operation is the command symmetrise

For specific orientations, e.g. for the cube orientations, symmetrisation leads to multiple identical orientations. This can be prevented by passing the option unique to the command symmetrise

## Crystal symmetries in computations

Note that all operation on orientations are preformed taking all symmetrically equivalent orientations into account. As an example consider the angle between a random orientation and all orientations symmetricall equivalent to the goss orientation

The value is the same for all orientations and equal to the smallest angle to one of the symmetrally equivalent orientations. This can be verified by computing the rotational angle ignoring symmetry.

Functions that respect crystal symmetry but allow to switch it off using the flag noSymmetry include dot, unique, calcCluster.