# Partial symmetry

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

*j*-th component S

_{j}. Such an operation is not one of the operations of the space

*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.