Hermann–Mauguin system

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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 Cn. nmm is the same group as Cnv. There are two ms because of two distinct types of mirror plane containing the n-fold axis. n22 is the same group as Dn. The other categories do not coincide with the Schoenflies system. ¯n is a group with an n-fold rotation-inversion axis and includes C3h as 6¯, S4 as 4¯, S6 as 3¯, and S2 as 1¯. n/m is the same group as Cnh except that C3h is regarded as ¯6. n2m is the same group as Dnd, except that D3h is regarded as 62m. n/m 2/m 2/m, abbreviated to n/mmm, is the same group as Dnh, except that D3h is regarded as ¯62m. (Unlike the Schoenflies system, the Hermann-Mauguin system regards the three-fold axis as a special case.) As regards the cubic groups, Oh is denoted m3m (or 4/m ¯3 2/m), O is denoted 432, Th is denoted m3 (or 2/m ¯3), Td is denoted ¯43m, 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.

Subjects: Chemistry — Physics.

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