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 diffraction pattern symmetries, such as 5-fold; these were not discovered until 1982 by Dan Shechtman.
2, 3, 4, and 6 fold crystals are more common than 5-fold.
( z1 have-degree :ARG1 ( z2 crystal :quant ( z3 and :op 2 :op 3 :op 4 :op 5 :op 6 :op ( z4 crystal ) ) ) :ARG2 ( z5 common ) :ARG3 ( z6 more ) :ARG4 ( z7 crystal :quant ( z8 times :quant 5 ) ) )