In fishy facts, I tried to update my canonicalization code to acommodate flipped orientations. However, it doesn't work because my meshes do not have flip symmetry.

For example, the tile [[N, W]] gets represented in the canonical form [[N, E]] with a horizontal flip. However, the north slice is rendered as if there is a connection to the east, and the west slice (which has been swapped with the east slice) is rendered as if there is a connection to the south, resulting in an incorrect appearance as the north and west sides have paths which don't connect to each other. In order for the decanonicalization to work, I would also need to retain information about how to change the meshes that cannot be flipped.

There's 63 tiles with only rotation symmetry and 56 with rotational and flip symmetry, so I think it would be easier to just not have flipping as part of the solution. I would have to write quite a lot of extra code to get it to work compared to the relatively simple case matching code for the other 7 cases.