In mathematics, a Coxeter group, named after H. S. M. Coxeter, is an abstract group that admits a formal description in terms of reflections (or kaleidoscopic...

Coxeter–Dynkin diagram (or Coxeter diagram, Coxeter graph) is a graph with numerically labeled edges (called branches) representing a Coxeter group or...

n Coxeter group has n mirrors and is represented by a Coxeter–Dynkin diagram. Coxeter notation offers a bracketed notation equivalent to the Coxeter diagram...

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...

In mathematics, a Coxeter element is an element of an irreducible Coxeter group which is a product of all simple reflections. The product depends on the...

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

Coxeter groups, so the affine symmetric groups are Coxeter groups, with the s i {\displaystyle s_{i}} as their Coxeter generating sets. Each Coxeter group...

infinite facets whose quotient group of their normal abelian subgroups is finite. They include the one-dimensional Coxeter group I ~ 1 {\displaystyle {\tilde...

is a deformation of the group algebra of a Coxeter group. Hecke algebras are quotients of the group rings of Artin braid groups. This connection found...

mathematics, the Coxeter complex, named after H. S. M. Coxeter, is a geometrical structure (a simplicial complex) associated to a Coxeter group. Coxeter complexes...

context—for example, whether one is discussing general Coxeter groups or complex reflection groups—but in all cases the collection of parabolic subgroups...

reflection group. Reflection groups also include Weyl groups and crystallographic Coxeter groups. While the orthogonal group is generated by reflections...

be visualized as symmetric orthographic projections in Coxeter planes of the E8 Coxeter group, and other subgroups. Symmetric orthographic projections...

{\displaystyle {\tilde {A}}_{3}} Coxeter group. The symmetry can be multiplied by the symmetry of rings in the Coxeter–Dynkin diagrams: The rectified cubic...

with Coxeter groups. Examples are free groups, free abelian groups, braid groups, and right-angled Artin–Tits groups, among others. The groups are named...

special kind of Coxeter diagram), the Weyl group (a concrete reflection group), or the abstract Coxeter group. Although the Weyl group is abstractly isomorphic...

theory of Coxeter groups, the symmetric group is the Coxeter group of type An and occurs as the Weyl group of the general linear group. In combinatorics...

mathematics, the longest element of a Coxeter group is the unique element of maximal length in a finite Coxeter group with respect to the chosen generating...

symmetry of the E8 group. It was discovered by Thorold Gosset, published in his 1900 paper. He called it an 8-ic semi-regular figure. Its Coxeter symbol is 421...

(7 3 2) triangle group, Coxeter group [7,3], orbifold (*732) contains these uniform tilings: The (8 3 2) triangle group, Coxeter group [8,3], orbifold...

In group theory, the Todd–Coxeter algorithm, created by J. A. Todd and H. S. M. Coxeter in 1936, is an algorithm for solving the coset enumeration problem...

four-dimensional crystal classes 1985 H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, Coxeter notation for 4D point groups 2003 John Conway and Smith, On Quaternions...

x1, x2, x3, x4) with -1 < xi < 1 for all i. n-cube Coxeter plane projections in the Bk Coxeter groups project into k-cube graphs, with power of two vertices...

Bi=M\wr \mathbb {Z} _{2}.\,} The Bimonster is also a quotient of the Coxeter group corresponding to the Dynkin diagram Y555, a Y-shaped graph with 16 nodes:...

groups in two dimensions. Other finite subgroups include: Permutation matrices (the Coxeter group An) Signed permutation matrices (the Coxeter group Bn);...

from the E6 group. It was first published in E. L. Elte's 1912 listing of semiregular polytopes, named as V72 (for its 72 vertices). Its Coxeter symbol is...

{A}}_{3}} Coxeter group. This honeycomb has four uniform constructions, with the truncated octahedral cells having different Coxeter groups and Wythoff...

{\displaystyle {\tilde {A}}_{3}} Coxeter group. The symmetry can be multiplied by the symmetry of rings in the Coxeter–Dynkin diagrams: The cantic cubic...

of 120. The full symmetry group is the Coxeter group of type H3. It may be represented by Coxeter notation [5,3] and Coxeter diagram . The set of rotational...

Groups of this type are identified by a parameter n, the dimension of the hypercube. As a Coxeter group it is of type Bn = Cn, and as a Weyl group it...