# Definition:Symmetry

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## Disambiguation

This page lists articles associated with the same title. If an internal link led you here, you may wish to change the link to point directly to the intended article.

**Symmetry** may refer to:

- Relation Theory:
- Symmetry (of a relation): whether a relation is
**symmetric**,**antisymmetric**,**asymmetric**or**non-symmetric**.

- Symmetry (of a relation): whether a relation is

- Mapping Theory:
- Symmetric Mapping: a mapping defined on a cartesian space whose values are preserved under permutation of its arguments:

- $\map f {x_1, x_2, \dotsc, x_n} = \map f {x_{\map \pi 1}, x_{\map \pi 2}, \dotsc x_{\map \pi n} }$ for all permuations $\pi$ on $\set {1, 2, \dotsc n}$

- Geometry:
- Symmetry mapping: A movement of a geometric figure so that it looks the same after it has been moved.

- Group Theory:
- Symmetry group: The set of all symmetry mappings of a geometric figure, the operation being composition of mappings.

## Linguistic Note

The word **symmetry** comes from Greek **συμμετρεῖν** (**symmetría**) meaning **measure together**.