I'm a huge fan of this and played for enough to understand the rotating in a triangular pattern to swap parity but not enough yet to solve puzzles without the picture of the final configuration :p
Is there a reference you used to design these knots, since I don't think Celtic knots are typically hexagonal?
One suggestion for making the game a bit easier to read is having slightly different gradients or colors on pieces of different types, so it's easier to see at a glance which two pieces are the same. I noticed though that there are pieces with the same edge types but different internal knotting (e.g. the straight Y piece and the knotted Y piece). Do those end up actually creating different knots in practice?