(a) High-energy x-ray diffraction pattern for a single grain of i-Gd-Cd, made up of gadolinium, a rare earth, and cadmium. The pattern shows a new kind of quasicrystal discovered in 2013, an icosahedral binary quasicrystal; note the 10-fold symmetry. (An icosahedron is a regular polyedron; see Spotlight 20.1 on page 829.) The investigators, who used mathematics to pinpoint the existence of such crystals, were exploring their magnetic properties. Rare earths are important for their magnetic properties; high-performance magnets made from them are used in windmill turbines, hybrid cars, cellphones, and headphones. (b) Photo of actual grain of i-Gd-Cd, showing its (imperfect) icosahedral shape.