# Partial symmetry

### From Online Dictionary of Crystallography

##### Revision as of 09:39, 17 November 2017 by BrianMcMahon (talk | contribs) (Tidied translations and corrected German (U. Mueller))

Symétrie partielle (*Fr*). Teilsymmetrie (*Ge*). Simmetria parziale (*It*). 部分対称 (*Ja*). Simetría parcial (*Sp*).

The symmetry operations of a space group are isometries operating on the whole crystal pattern and are also called **total operations** or **global operations**. More generally, the crystal space can be divided in *N* components S_{1} to S_{N}, and a coincidence operation φ(S_{i})→S_{j} can act on just the *i*th component S_{i} to bring it to coincide with the *j*th component S_{j}. Such an operation is not one of the operations of the space group of the crystal because it is not a coincidence operation of the whole crystal space; it is not even defined, in general, for any component *k* different from *i*. It is called a **partial operation**: from the mathematical viewpoint, partial operations are space-groupoid operations.

When *i* = *j*, *i.e.* when the operation is φ(S_{i})→S_{i} and brings a component to coincide with itself, the partial operation is of special type and is called **local**. A local operation is in fact a symmetry operation, which is defined only on a part of the crystal space: local operations may constitute a subperiodic group.