# Point group

## Definition

### Symbol-free definition

A **point group** in dimension is a subgroup of the orthogonal group , or equivalently, a group of geometric symmetries which leave a particular point fixed.

When we use the term **point group**, we usually mean not just the abstract group, but rather its embedding as a subgroup of the orthogonal group.

A point group can thus also be regarded as a faithful linear representation of a group in terms of only isometries.

## Related notions

- Rosette group: A point group in two dimensions
- Molecular point group: A point group in three dimensions, so named because these groups describe the symmetries of molecules
- Space group
- Crystallographic point group