Is there a systematic way to find solutions of the Yang-Baxter equation independent of the context (statistical physics in 2d or braids etc) ? And if yes can someone please a) sketch the procedure, b) provide some reference, c) comment on possible generalization to the tetrahedron equations?

As far as b) is concerned I have only seen some solutions in terms of statistical physics (e.g. Van Nieuwenhuizen notes on QFT). So, I would really find extremely useful some reference on the subject.

Thanks a lot in advance.