By quasi crystals we mean materials with a non crystallographic symmetry group, e.g. including a pentagonal or decagonal symmetry axis. Such symmetry groups do not lead to perfect translational invariant lattices and hence are not crystals.
Setting up a non standard symmetry group can be done by specifying all its symmetry elements. To illustrate this definition lets consider the symmetry group corresponding to the dodecaeder which is generated by a 5 fold and a 3 fold symmetry axis.
Many of the MTEX methods do work also with quasi symmetries. E.g. we can identify the fundamental sector by
the fundamental region is orientation space, which is exactly a dodecaeder,
or define an approbiate color key
We may also choose a different setup where the 5 fold axis is aligned parallel to z