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by zokier
1185 days ago
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> 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. |
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