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 be formed from various elements, such as aluminum and copper, and are known for their unusual symmetry, which can include five-fold rotational symmetry that is not possible in conventional crystals. Discovered in the 1980s by Dan Shechtman, quasicrystals challenge the traditional understanding of crystallography. They have applications in various fields, including materials science and nanotechnology, due to their unique properties, such as increased hardness and resistance to wear.