Danny Shechtman discovered quasicrystals in 1982. They produce a sharp diffraction pattern like other crystals, but they have fivefold symmetry, which is “forbidden”. You cannot tesselate pentagons, after all. Hexagons, yes. Squares, of course…the discovery of these quasicrystals turned on its head our understanding of what it means to be a crystal. A crystal needn’t be regular as these quasicrystals show, like the Moorish artwork of ancient palaces and the patterns described by Roger Penrose et al. The discovery earned Shechtman the Nobel Prize for Chemistry 2011 on 5th October. Here he is discussing the discovery and its implications:
Thanks to Simon Frantz for sharing this Technion video via Twitter.