Quasicrystal

Summary

A quasicrystal is a structure that is ordered but not periodic. Its diffraction pattern shows sharp peaks, as for a crystal, yet no translation maps it onto itself. Quasicrystals can have symmetries that no periodic crystal can have, such as five-fold or ten-fold rotations. Dan Shechtman observed the first one, an aluminium–manganese alloy with icosahedral symmetry, in 1982, and received the Nobel Prize in Chemistry in 2011. Mathematical models include the vertex sets of the Penrose tiling and other aperiodic tilings.