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A Triangular Tiling

A remarkable non-periodic triangular tiling, discovered by Charles Radin (see C. Radin, The pinwheel tilings of the plane, Annals of Math. 139(1994), 661-702, pinwheel) was used as the basis of this foyer tiling. It begins with a large square tile cut in half then the two pieces were cut down a diagonal. The final triangle has sides of length (1,2,√5). Note that the correct number of left-handed and right-handed right triangles were required to cover this space. The tiling is self-similar, on an increasing scale and furthermore the triangles point in an infinite number of different directions---thus ensuring aperiodicity.

Ralph Buchholz

19 March 2013