Relation With Coxeter Groups
A reflection group W admits a presentation of a special kind discovered and studied by H.S.M. Coxeter. The reflections in the faces of a fixed fundamental "chamber" are generators ri of W of order 2. All relations between them formally follow from the relations
expressing the fact that the product of the reflections ri and rj in two hyperplanes Hi and Hj meeting at an angle is a rotation by the angle fixing the subspace Hi ∩ Hj of codimension 2. Thus, viewed as an abstract group, every reflection group is a Coxeter group.
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