Explore: Coxeter Groups

Coxeter groups are precisely the finite Euclidean reflection groups; for example, the symmetry group of each regular polyhedron is a finite Coxeter group

Coxeter notation (also Coxeter symbol) is a system of classifying symmetry groups, describing the angles between fundamental reflections of a Coxeter

yielding 10 groups. The subset of pure reflectional point groups, defined by 1 or 2 mirrors, can also be given by their Coxeter group and related polygons

geometry and group theory are named after him, including the Coxeter graph, Coxeter groups, Coxeter's loxodromic sequence of tangent circles, Coxeter–Dynkin

deformation of the group algebra of a Coxeter group. The Hecke algebra can also be viewed as a q-analog of the group algebra of a Coxeter group. Hecke algebras

Coxeter number. They are named after British-Canadian geometer H.S.M. Coxeter, who introduced the groups in 1934 as abstractions of reflection groups

passing through the same point are the finite Coxeter groups, represented by Coxeter notation. The point groups in three dimensions are widely used in chemistry

reflection group. In fact it turns out that most finite reflection groups are Weyl groups. Abstractly, Weyl groups are finite Coxeter groups, and are important

symmetric group of permutations, the dihedral groups, and more generally all finite real reflection groups (the Coxeter groups or Weyl groups, including

Unsolved problem in mathematics Given two Coxeter groups Γ 1 {\displaystyle \Gamma _{1}} and Γ 2 {\displaystyle \Gamma _{2}} , decide whether W ( Γ 1 )