Penrose tiling with sharp 5-fold diffraction — long-range order without periodicity
Quasicrystals (Shechtman et al., 1984 — Nobel 2011) have sharp Bragg peaks arranged with icosahedral or 5-fold symmetry, forbidden for any periodic lattice. The Penrose tiling is the canonical 2D quasicrystal: two tile shapes (fat and thin rhombi) fill the plane aperiodically, with diffraction described by six irrational reciprocal-lattice vectors related by τ = (1+√5)/2.