Penrose Tilings and Quasicrystals Revisited

Abstract Roger Penrose’s ingenious invention of five-fold symmetric, non-periodic tilings has inspired the proposal of a new form of solid, known as a quasicrystal. Quasicrystals are solids with quasiperiodic atomic structures and symmetries forbidden to ordinary, periodic crystals, e.g., three-dimensional icosahedral symmetry. Here we discuss some new properties of Penrose tilings uncovered in recent months which suggest a new, simple picture of the structure of quasicrystals and shed new light on why they form.