text: The first representations of perfect quasicrystalline patterns can be found in several early Islamic works of art and architecture such as the Gunbad-i-Kabud tomb tower, the Darb-e Imam shrine and the Al-Attarine Madrasa. 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 1974 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 theoretically 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, AlMn, 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 to find out what it is".
  The observation of the ten-fold diffraction pattern lay unexplained for two years until the spring of 1984, when Blech asked Shechtman to show him his results again. A quick study of Shechtman's results showed that the common explanation for a ten-fold symmetrical diffraction pattern, a type of crystal twinning, was ruled out by his experiments. Therefore, Blech looked for a new structure containing cells connected to each other by defined angles and distances but without translational periodicity. He decided to use a computer simulation to calculate the diffraction intensity from a cluster of such a material, which he termed as "multiple polyhedral", and found a ten-fold structure similar to what was observed. The multiple polyhedral structure was termed later by many researchers as icosahedral glass.
  Shechtman accepted Blechs discovery of a new type of material and chose to publish his observation in a paper entitled "The Microstructure of Rapidly Solidified AlMn", which was written around June 1984 and published in a 1985 edition of Metallurgical Transactions A. Meanwhile, on seeing the draft of the paper, John Cahn suggested that Shechtmans experimental results merit a fast publication in a more appropriate scientific journal. Shechtman agreed and, in hindsight, called this fast publication "a winning move”. This paper, published in the Physical Review Letters, repeated Shechtman's observation and used the same illustrations as the original paper.
  Originally, the new form of matter was dubbed "Shechtmanite". The term "quasicrystal" was first used in print by Steinhardt and Levine shortly after Shechtman's paper was published.
  Also in 1985, Ishimasa et al. reported twelvefold symmetry in Ni-Cr particles. Soon, eightfold diffraction patterns were recorded in V-Ni-Si and Cr-Ni-Si alloys. Over the years, hundreds of quasicrystals with various compositions and different symmetries have been discovered. The first quasicrystalline materials were thermodynamically unstable—when heated, they formed regular crystals. However, in 1987, the first of many stable quasicrystals were discovered, making it possible to produce large samples for study and applications.
  In 1992, the International Union of Crystallography altered its definition of a crystal, reducing it to the ability to produce a clear-cut diffraction pattern and acknowledging the possibility of the ordering to be either periodic or aperiodic.
  In 2001, Paul Steinhardt of Princeton University hypothesized that quasicrystals could exist in nature and developed a method of recognition, inviting all the mineralogical collections of the world to identify any badly cataloged crystals. In 2007 Steinhardt received a reply by Luca Bindi, who found a quasicrystalline specimen from Khatyrka in the University of Florence Mineralogical Collection. The crystal samples were sent to Princeton University for other tests, and in late 2009, Steinhardt confirmed its quasicrystalline character. This quasicrystal, with a composition of AlCuFe, was named icosahedrite and it was approved by the International Mineralogical Association in 2010. Analysis indicates it may be meteoritic in origin, possibly delivered from a carbonaceous chondrite asteroid. In 2011, Bindi, Steinhardt, and a team of specialists found more icosahedrite samples from Khatyrka. A further study of Khatyrka meteorites revealed micron-sized grains of another natural quasicrystal, which has a ten-fold symmetry and a chemical formula of AlNiFe. This quasicrystal is stable in a narrow temperature range, from 1120 to 1200 K at ambient pressure, which suggests that natural quasicrystals are formed by rapid quenching of a meteorite heated during an impact-induced shock.
  Shechtman was awarded the Nobel Prize in Chemistry in 2011 for his work on quasicrystals. "His discovery of quasicrystals revealed a new principle for packing of atoms and molecules," stated the Nobel Committee and pointed that "this led to a paradigm shift within chemistry." In 2014, Post of Israel issued a stamp dedicated to quasicrystals and the 2011 Nobel Prize.
  While the first quasicrystals discovered were made out of intermetallic components, later on quasicrystals were also discovered in soft-matter and molecular systems. Soft quasicrystal structures have been found in supramolecular dendrimer liquids and ABC Star Polymers in 2004 and 2007. In 2009, it was found that thin-film quasicrystals can be formed by self-assembly of uniformly shaped, nano-sized molecular units at an air-liquid interface. It was demonstrated that these units can be both inorganic and organic. Additionally in the 2010s, two-dimensional molecular quasicrystals were discovered, driven by intermolecular interactions and interface-interactions.
  In 2018, chemists from Brown University announced the successful creation of a self-constructing lattice structure based on a strangely shaped quantum dot. While single-component quasicrystal lattices have been previously predicted mathematically and in computer simulations, they had not been demonstrated prior to this.