|By Paul J. Steinhardt et al. - http://www.nature.com/srep/2015/150313/srep09111/full/srep09111.html, CC BY 4.0, https://commons.wikimedia.org/w/index.php?curid=40522020|
Quasicrystals1,2, short for quasiperiodic crystals, are solids able to violate the conventional rules of crystallography because their structure is “quasiperiodic” rather than periodic; that is, their atomic density can be described by a finite sum of periodic functions with periods whose ratio is irrational. Their diffraction pattern consists of true Bragg peaks whose positions can be expressed as integer linear combinations of D integer linearly independent wavevectors where D is greater than the number of space dimensions. Among the quasicrystals made in the laboratory, many exhibit a crystallographically forbidden, three-dimensional icosahedral symmetry defined by D = 6 integer linearly independent wavevectors. See: Collisions in outer space produced an icosahedral phase in the Khatyrka meteorite never observed previously in the laboratoryBindi, L. et al. Collisions in outer space produced an icosahedral phase in the Khatyrka meteorite never observed previously in the laboratory. Sci. Rep. 6, 38117; doi: 10.1038/srep38117 (2016).