1.78: 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 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.