From Tiling Floors to Quasicrystals
DOI link for From Tiling Floors to Quasicrystals
From Tiling Floors to Quasicrystals book
No-one ever suggested that tiling floors with equal-sized square tiles was either difficult or intellectually stimulating. This particular solution to the problem of 'tiling the plane' must surely have been self-evident to the first human who ever gave it a thought. The tiling problem for the six-sided convex hexagon, for which the bees have already found the most symmetric answer, was also discussed exhaustively by Reinhardt in his 1918 doctoral dissertation. For convex polygons with more than six sides the problem, becomes much less difficult since a proof has been known for quite some time that no such polygon exists that can pave the plane in the manner required. The first decagonal quasicrystal was identified soon after the discovery of the original aluminum-manganese icosahedral system. It was, in fact, obtained in the very same alloy by cooling at a somewhat slower rate than was necessary to obtain the icosahedral quasicrystal.