Apt for questions related to reflection group (discrete group which is generated by a set of reflections of a finite-dimensional Euclidean space).
In group theory and geometry, a reflection group is a discrete group which is generated by a set of reflections of a finite-dimensional Euclidean space. The symmetry group of a regular polytope or of a tiling of the Euclidean space by congruent copies of a regular polytope is necessarily a reflection group. Reflection groups also include Weyl groups and crystallographic Coxeter groups. While the orthogonal group is generated by reflections (by the Cartan–Dieudonné theorem), it is a continuous group (indeed, Lie group), not a discrete group, and is generally considered separately.
Let $E$ be a finite-dimensional Euclidean space. A finite reflection group is a subgroup of the general linear group of $E$ which is generated by a set of orthogonal reflections across hyperplanes passing through the origin. An affine reflection group is a discrete subgroup of the affine group of $E$ that is generated by a set of affine reflections of $E$ (without the requirement that the reflection hyperplanes pass through the origin).
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