Quasicrystals are a unique type of solid material that exhibit an ordered structure but do not have a repeating pattern like traditional crystals. They can form complex arrangements that are often symmetrical, displaying patterns that can be described using mathematical concepts such as Penrose tiling. This non-repeating order gives quasicrystals their distinctive properties. Discovered in the 1980s by Dan Shechtman, quasicrystals challenge the conventional understanding of crystallography. They can possess unusual physical properties, such as low thermal conductivity and high strength, making them of interest for various applications, including coatings and materials science.