Coxeter diagrams are graphical representations used to describe abstract geometric structures known as Coxeter groups. These diagrams consist of nodes and edges, where each node represents a reflection or a generator of the group, and the edges indicate the angles between these reflections. The diagrams help visualize the relationships and symmetries within the group. Each edge in a Coxeter diagram can be labeled with a number that specifies the order of the corresponding reflections. If no label is present, it is assumed to be 3. Coxeter diagrams are widely used in various fields, including geometry, algebra, and combinatorics, to study symmetrical properties of shapes and spaces.