On an old paper, I found an interesting representation of some symmetry operations: stereographs.
Online I found a set of symmetry operations and related stereographs (see: http://newton.ex.ac.uk/research/qsystems/people/goss/symmetry/Stereographs.html), yet it's not clear to me how the representation is related to the symmetry operations (or: how are the representations obtained?).
Some samples from the website linked above:
I would like to understand the geometrical (and symbolical) meaning of a stereograph, in order to relate non-mnemonically it to its symmetry operation