I propose to classify opening patterns (fuseki) according to the first four moves, assuming they are either star points or 3-4 points. That already makes for ~70 different distributions, including symmetry. Usually, openings are classified from Black's perspective, as Black has the initiative. We usually don't differentiate White's choices to play 4-4 or 3-4 and so we can simplify the classification by assuming two white star points.
Due to symmetry, there's only one diagonal pattern with one 3-4 stone.