History On July 16, 1945, in Alamogordo, New Mexico, the Trinity nuclear bomb test produced icosahedral quasicrystals. They went unnoticed at the time of the test but were later identified in samples of red Trinitite, a glass-like substance formed from fused sand and copper transmission lines. Identified in 2021, they are the oldest known anthropogenic quasicrystals. In 1961, Hao Wang asked whether determining if a set of tiles admits a tiling of the plane is an algorithmically unsolvable problem or not. He conjectured that it is solvable, relying on the hypothesis that every set of tiles that can tile the plane can do it periodically (hence, it would suffice to try to tile bigger and bigger patterns until obtaining one that tiles periodically). Nevertheless, two years later, his student Robert Berger constructed a set of some 20,000 square tiles (now called "Wang tiles") that can tile the plane but not in a periodic fashion. As further aperiodic sets of tiles were discovered, sets with fewer and fewer shapes were found. In 1976 Roger Penrose discovered a set of just two tiles, now referred to as Penrose tiles, that produced only non-periodic tilings of the plane. These tilings displayed instances of fivefold symmetry. One year later Alan Mackay showed experimentally that the diffraction pattern from the Penrose tiling had a two-dimensional Fourier transform consisting of sharp 'delta' peaks arranged in a fivefold symmetric pattern. Around the same time, Robert Ammann created a set of aperiodic tiles that produced eightfold symmetry. In 1972 de Wolf and van Aalst reported that the diffraction pattern produced by a crystal of sodium carbonate cannot be labeled with three indices but needed one more, which implied that the underlying structure had four dimensions in reciprocal space. Other puzzling cases have been reported, but until the concept of quasicrystal came to be established, they were explained away or denied. Shechtman first observed ten-fold electron diffraction patterns in 1982, while conducting a routine study of an aluminium–manganese alloy, Al6Mn, at the US National Bureau of Standards (later NIST). Shechtman related his observation to Ilan Blech, who responded that such diffractions had been seen before. Around that time, Shechtman also related his finding to John W. Cahn of the NIST, who did not offer any explanation and challenged him to solve the observation. Shechtman quoted Cahn as saying: "Danny, this material is telling us something, and I challenge you