Suppose the side length of the square is 12.
A basic triangle is a collection of tiles which form a right triangle with sides of length 6 and 12.
Note that all vertices in the original tiling have integer coordinates. In fact, this is true in any tiling of the square (why?). It can be shown that there is a unique partition of the Stomach tiles which can form four basic triangles, which we call 1, 2, 3 and 4.



The core consists of 24 configurations that are made up of these four basic triangles, in which triangle 4 is partitioned by two intersecting straight lines. Here is the core (where the labeling is determined by the order in which the basic triangles are hit as you go from top to bottom, and x' denotes that triangle x has been turned over).


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