At the Tiling Database:
There are 3, 20, 198, 1390 non-tiling polyominoes of order 7 to 10.
There are 4, 37, 381, 2717 non-tiling polyhexes of order 6 to 9.
There are 1, 0, 20, 103, 594, 1192, 6290 non-tiling polyiamonds of order 7 to 13.
Have these non-tilers had their Heesch numbers determined? A non-tiler that can surround itself is Heesch-1. If a second complete ring can be made, that's Heesch-2.
What simple polyforms are Heesch-2?
