Point group
From Groupprops
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