Coxeter groups
Coxeter groups are mathematical structures that arise in the study of symmetry and geometry. They are defined by a set of generators and relations, which describe how these generators can be combined. Each generator corresponds to a reflection across a hyperplane in a Euclidean space, and the relations specify how these reflections interact.
These groups are named after the mathematician H.S.M. Coxeter, who explored their properties in the context of polytopes and geometric structures. Coxeter groups can be classified into finite and infinite types, and they play a significant role in various areas of mathematics, including group theory and combinatorial geometry.