
A remarkable nonperiodic triangular tiling, discovered by Charles Radin (see C. Radin, The pinwheel tilings of the plane, Annals of Math. 139(1994), 661702, 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 lefthanded and righthanded right triangles were required to cover this space. The tiling is selfsimilar, on an increasing scale and furthermore the triangles point in an infinite number of different directionsthus ensuring aperiodicity. Ralph Buchholz 19 March 2013 