A Coxeter group is a special type of group that can be defined geometrically using reflections in Euclidean spaces. These groups are named after H.S.M. Coxeter, who studied their properties and relationships to various geometrical structures. ### Basic Definition: A Coxeter group is defined by a set of generators subjected to specific relations. These relations are based on the angles between the reflections corresponding to the generators.
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A Coxeter group is a group with a presentationwhere and for . The pair consisting of and its distinguished generating reflections is a Coxeter system.