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Tametsi isn't integrated tightly with Steam, so it's not currently possible to include achievements. Adding some new levels (outside of the main 100) that change the basic rules is a good idea, though.
...Actually on that note... for tilings that can have the diagonal adjacency flag, if for non-touching puzzles you round off corners at all intersections, so that such tiles visibly aren't touching, you don't need to show a flag on screen for when they are. Maybe simpler?
The game works just fine with arbitrary polygons, and even arbitrary neighborhoods (every tile could be a range-2 hint, for example), except for the burden it puts on the player. I think keeping track of a tile's neighbors in a general polyomino tiling would cause similar problems.
I'm in the process of adding support for more puzzles, so some of these ideas might show up in the game later. Thank you for the suggestions!
You mentioned more puzzles or mechanics, looking forward to whatever you may have in store!
But this game is good enough that I'll play it even without them ;)
The standard way to depict this would be to use arrows along the borders of the board, as in the square diagram here: https://en.wikipedia.org/wiki/Klein_bottle
The Witness includes some cylindrical puzzles, and it was an interesting twist, but they weren't one of my favorite parts of that game. I'm not sure whether I will try something like that or not.