3D-rotations lie at the core multigrain crystallography, texture analysis, and many other topics in materials science.

Typically, one describes the orientation of a crystal lattice by a set of rotations relative to an external reference frame. Unfortunately, there are many ways to do so!

If you want to dig into this topic, you may look at

• Consistent representations of and conversions between 3D rotations, D Rowenhorst et al 2015 Modelling Simul. Mater. Sci. Eng. 23 083501 https://doi.org/10.1088/0965-0393/23/8/083501