Quasicrystals are unique, ordered structures that were once thought to be impossible according to traditional crystallography rules. These materials exhibit symmetries that are forbidden in traditional periodic crystals, such as rotational symmetries of 5-fold, 8-fold, or 12-fold axes. Quasicrystals have attracted much attention in materials science due to their fascinating properties, such as low thermal conductivity, high hardness, and high corrosion resistance. They have potential applications in a wide range of fields, including catalysis, thermoelectric materials, and coatings. Research on quasicrystals aims to understand their fundamental properties, synthesis methods, and potential applications in various industries.