Among the 268 possible tilings of a 12 x 12 square, there are 24 special tilings which are called core tilings.

From each core tiling there are at least 4 (and sometimes as many as 17) other tilings which can be reached by local moves.

The set of tilings reachable this way from a core tiling T will be called the cluster associated to T. Here we list 24 clusters in lexicographical order:

1234| 123'4' | 1243 | 124'3'
1324 | 132'4' | 1342 | 134'2'
1423 | 142'3' | 1432 | 143'2'
2134 | 213'4' | 2143 | 214'3'
3124 | 312'4' | 3142 | 314'2'
4123 | 412'3' | 4132 | 413'2'

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