# Geometric element

### From Online Dictionary of Crystallography

Élément géométrique (Fr); Elemento geometrico (It); 幾何的要素 (Ja).

A geometric element is an element in space (plane, line, point, or a combination of these) about which a symmetry operation is performed. Geometric elements are classified on the basis of the dimensionality N of the space on which they act, the upper limit on the dimensionality of the symmetry element being N-1.

## One-dimensional space

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

## Two-dimensional space

In this space, two types of geometric elements exist: zero and one-dimensional:

• rotations 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: zero, one- and two-dimensional:

• inversion centres
• rotations 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.