The tiles seem like they can only join at one spot to one spot so I don’t think it would even be possible to lay them incorrectly unless you straight were jamming incorrect sides together.
> First we produce a list of possible neighbours of the hat polykite in a tiling. There are 58 possible neighbours when we only require such a neighbour not to intersect the original polykite; these are shown in Figure B.1, with that original polykite shaded. The first 41 of these neighbours remain in consideration for the enumeration of 1-patches. The final 17 are immediately eliminated (in the order shown) because they cannot be extended to a tiling: either there is no possible neighbour that can contain the shaded kite (without resulting in an intersection, or a pair of tiles that were previously eliminated as possible neighbours), or we eliminated Y as a neighbour of X and so can also eliminate X as a neighbour of Y.
From the preprint. It is definitely possible to lay the tiles so that they do not tile anymore.
From the preprint. It is definitely possible to lay the tiles so that they do not tile anymore.