# Wyckoff position

A **Wyckoff position** of a space group G consists of all points *X* for which the site-symmetry groups are conjugate

Each Wyckoff positon of a space group is labeled by a letter which is called the *Wyckoff letter*.

The number of different Wyckoff positions of each space group is finite, the *p*2*mm*) and 27 for space groups (realized in *Pmmm*).

There is a total of 72 Wyckoff

The transfer of Wyckoff positions from individual space groups to space-group types is not unique because Wyckoff positions with the same type of site-symmetry group may be exchanged in different space groups of the same type. This is no longer true when one makes use of Wyckoff sets.

### Wyckoff positions of point groups

By analogy to the Wyckoff positions of space groups, Wyckoff positions of point groups have been defined too: here the term "position" indicates the position of face poles (form face

### History

The term *Wykcoff position* takes its origin from the first English collection of equivalent positions in space groups, which appeared in *The analytical expression of the results of the theory of space groups* by Ralph W.G. Wyckoff, published by *International Tables for Crystallography*.

### See also

- Sections 8.3.2 and 10.1.2.2 of the
*International Tables of Crystallography*, Volume A