Mathematicians have long wondered if there was an "einstein tile" – a tile that could be used only to make a non-repeating pattern on an infinite surface. An amateur mathematician named David Smith recently developed a 13-sided tile, nicknamed "the hat," that fits the bill.
Compared to the tiles created by renowned mathematician Roger Penrose, "the hat" stands out because it is a single tile rather than a pair of tiles. Moreover, it is unique among tiles that can create repeating and non-repeating patterns because it cannot create repeating patterns.
[Via Smithsonian]
