## Quick Reference

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*. There are two

_{nv}*m*s because of two distinct types of mirror plane containing the

*n*-fold axis.

*n*22 is the same group as

*D*. The other categories do not coincide with the Schoenflies system.

_{n}*¯n*is a group with an

*n*-fold rotation-inversion axis and includes

*C*

_{3}

*as 6¯,*

_{h}*S*

_{4}as 4¯,

*S*

_{6}as 3¯, and

*S*

_{2}as 1¯.

*n*/

*m*is the same group as

*C*except that

_{nh}*C*

_{3}

*is regarded as ¯6.*

_{h}*n*2

*m*is the same group as

*D*, except that

_{nd}*D*

_{3}

*is regarded as 62*

_{h}*m*.

*n*/

*m*2/

*m*2/

*m*, abbreviated to

*n*/

*mmm*, is the same group as

*D*, except that

_{nh}*D*

_{3}

*is regarded as ¯62*

_{h}*m*. (Unlike the Schoenflies system, the Hermann-Mauguin system regards the three-fold axis as a special case.) As regards the cubic groups,

*O*is denoted

_{h}*m*3

*m*(or 4/

*m*¯3 2/

*m*),

*O*is denoted 432,

*T*is denoted

_{h}*m*3 (or 2/

*m*¯3),

*T*is denoted ¯43

_{d}*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.

*Subjects:*
Chemistry — Physics.