A notation used to describe the symmetry of point groups. In contrast to the Schoenflies system, which is used for isolated molecules (e.g. in spectroscopy), the Hermann–Mauguin system is used in crystallography. Some of the categories are the same as the Schoenflies system. n is the same group as C_n. nmm is the same group as C_nv. There are two ms because of two distinct types of mirror plane containing the n-fold axis. n22 is the same group as D_n. The other categories do not coincide with the Schoenflies system. n̄ is a group with an n-fold rotation–inversion axis and includes C_3h as $\overline{6}$, S₄ as $\overline{4}$, S₆ as $\overline{3}$, and S₂ as $\overline{1}$. n/m is the same group as C_nh except that C_3h is regarded as $\overline{6}$. n2m is the same group as D_nd, except that D_3h is regarded as 62m. n/m 2/m 2/m, abbreviated to n/mmm, is the same group as D_nh, except that D_3h is regarded as $\overline{6}$ $\overline{2}$m. (Unlike the Schoenflies system, the Hermann–Mauguin system regards the three-fold axis as a special case.) As regards the cubic groups, O_h is denoted m3m (or 4/m $\overline{3}$ 2/m), O is denoted 432, T_h is denoted m3 (or 2/m $\overline{3}$), T_d is denoted $\overline{4}$$\overline{3}m$, and T is denoted 23. In the Hermann–Mauguin system all the cubic groups have 3 as the second number because of the three-fold axis that occurs in all cubic groups. It is named after the German crystallographer Carl Hermann (1898–1961) and the French mineralogist Charles-Victor Mauguin (1878–1958), who devised this notation in the late 1920s and early 1930s.