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A rational n-tiling of the unit square is a collection of n triangles with rational side length whose union is the unit square and whose intersections are at most their boundary edges. It is known that there are no rational 2-tilings or 3-tilings of the unit square, and that there are rational 4- and 5-tilings. The nature of those tilings is the subject of current research. In this project we give a combinatorial basis for rational n-tilings and explore rational 6-tilings of the unit square.
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Dorpalen-Barry, Galen, "Rational Tilings of the Unit Square" (2015). Senior Projects Spring 2015. 136.