For context, I'm an undergrad studying math. In one of my courses, my professor taught us about finite projective planes and, in particular, the Fano plane. I've skimmed the Wikipedia page and read about the Transylvania lottery problem. My professor also mentioned something about the Fano plane's usefulness in tournament and meeting scheduling, but he didn't elaborate much further.
My question is: what are some practical applications of the Fano plane? What sorts of problems can it solve, or more generally, what sort of problems do FPPs help us with?
All insight, comments, and questions are appreciated.