# Twin operation

### From Online Dictionary of Crystallography

Opération de maclage (*Fr*). Operazione di geminazione (*It*). 双晶操作 (*Ja*).

The operation (action) of an element of symmetry that generates a *twin*.

Let *H _{i}* be the oriented point group of the

*i*-th individual of a twin. The intersection group of the oriented vector point groups

*H*of the individuals is indicated as

_{i}*H** = ∩

_{i}

*H*. The symmetry of a twin is identified in vector space by a point group

_{i}*K*which is a supergroup of

*H**. The coset decomposition of

*K*with respect to

*H** gives the possible twin laws, each coset representing a twin law, and each operation in a coset representing a twin operation; the operations in a coset are equivalent under the operations of

*H**.

Operations in *H* describe the vector point symmetry of the individuals, whereas those in the cosets obtained by decomposing *K* in terms of *H** connect the different individuals. To underline their different nature, the twin operations are often associated with a 'colour' and *K* is a thus a chromatic vector point group, known as a *twin point group*.

## See also

- Chapter 3.3 of
*International Tables for Crystallography, Volume D*