Reflection Group

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.

Read more about Reflection Group:  Definition, Kaleidoscopes, Relation With Coxeter Groups, Finite Fields, Generalizations

Famous quotes containing the words reflection and/or group:

    It is conceivable at least that a late generation, such as we presumably are, has particular need of the sketch, in order not to be strangled to death by inherited conceptions which preclude new births.... The sketch has direction, but no ending; the sketch as reflection of a view of life that is no longer conclusive, or is not yet conclusive.
    Max Frisch (1911–1991)

    The conflict between the need to belong to a group and the need to be seen as unique and individual is the dominant struggle of adolescence.
    Jeanne Elium (20th century)