# Symmetry element

عنصر التماثل (Ar). Élément de symétrie (Fr). Symmetrieelement (Ge). Elemento di simmetria (It). 対称要素 (Ja). Elemento de simetría (Sp).

A symmetry element (of a given crystal structure or object) is defined as a concept with a double meaning, namely the combination of a geometric element with the set of symmetry operations having this geometric element in common (termed its element set). Together with the identity and the translations, for which a geometric element is not defined, the element sets cover all symmetry operations.

## One-dimensional space

The only symmetry element that exists in this space is the reflection point (mirror point).

## Two-dimensional space

In this space, two types of symmetry elements exist:

• rotation points
• reflection lines (mirror lines)

The inversion centre (point) does not exist in spaces of even number of dimensions.

## Three-dimensional space

In this space, three types of geometric elements exist:

• inversion centres
• rotation axes
• reflection planes (mirror planes)

For roto-inversion operations, the geometric element is a combination of a line, about which the rotation is performed, and a point (inversion point) with respect to which the inversion is performed.