1 pair needs to be the same for permutations.
And both sides need to be the same on any 1 piece for orientation.
Yes, that makes a lot of sense, thanks.
But what about 2 pairs of identical edges and no symmetrical edges, or 2 symmetrical edges and no pairs of identical edges? Or what about 3 identical edges (i.e., a triplet) with no symmetrical edges? Would these work? Do you really need at least one of each type to ensure that the puzzle is always solveable, or can they substitute for each other?