Hermann-Mauguin designation

The coordinate system of reference is taken with the vertical principal axis (z axis). Schoenflies symbols are rather compact—they designate only a minimum of the symmetry elements present in the following way (the corresponding Hermann-Mauguin symbols are given in brackets) ... 

The symbol 3/m is used here because it is descriptive of the two operations that are being discussed. Conventionally this point group is designated by the equivalent Hermann-Mauguin symbol 6. 

The Hermann-Mauguin notation for the description of point group symmetry (in contrast to the Schonflies system used in Chapter 6) is widely adopted in crystallography. An n-fold rotation axis is simply designated as n. An object is said to possess an n-fold inversion axis h if it can be brought into an equivalent configuration by a rotation of 360°/n in combination with inversion through a... 

Use arabic numerals or combinations of numerals and the italic letter m to designate the 32 crystallographic point groups (Hermann-Mauguin). The number is the degree of the rotation, and m stands for mirror plane. Use an overbar to indicate rotation inversion. 

Designate space groups by a combination of unit cell type and point group symbol, modified to include screw axes and glide planes (Hermann-Mauguin) 230 space groups are possible. Use italic type for conventional types of unit cells (or Bravais lattices) P, primitive I, body-centered A, A-face-centered B, B-face-centered C, C-face-centered P, all faces centered and R, rhombohedral. 

The complete designation of the symmetry of a crystal requires the correct assignment of axes and identification of (he symmetry elements. There are a total of 32 different combinations of symmetry elements. Each of these has a unique Hermann-Mauguin notation or point group and is called a crystal class. The 32 crystal classes can be divided into six crystal systems. We will (ry to give you an appreciation of point groups and crystal classes, but our main emphasis will be on the more general crystal systems. 

Designation Typical example (Mineral name) Crystal system Hermann-Mauguin Pearson s... 

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