High Quality Content by WIKIPEDIA articles! The crystallographic restriction theorem in its basic form was based on the observation that the rotational symmetries of a crystal are usually limited to 2-fold, 3-fold, 4-fold, and 6-fold. However, quasicrystals can occur with other symmetries, such as 5-fold; these were not discovered until 1982, when a diffraction pattern out off a quasicrystal was first seen by the Israeli scientist Dan Shechtman, who won the 2011 Nobel Prize in Chemistry for his discovery.