In crystallography, due to the crystallographic restriction theorem, n is restricted to the values of 1, 2, 3, 4, or 6. The noncrystallographic groups are shown with grayed backgrounds. D 4d and D 6d are also forbidden because they contain improper rotations with n = 8 and 12 respectively. The 27 point groups in the table plus T, T d, T h, O and O h constitute 32 crystallographic point groups.