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...

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...

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...

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

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...

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...

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...

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

is the author of two books that include The Geometry and Topology of Coxeter Groups and Multiaxial Actions on Manifolds. His notable contributions to the...

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

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

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

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

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

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:...

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...

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...

(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...

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

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

'pentachoron, pentatope, pentahedroid, tetrahedral pyramid, or 4-simplex (Coxeter's α 4 {\displaystyle \alpha _{4}} polytope), the simplest possible convex...

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...

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

Dynkin diagram for F4 is: . Its Weyl/Coxeter group G = W(F4) is the symmetry group of the 24-cell: it is a solvable group of order 1152. It has minimal faithful...

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

be visualized as symmetric orthographic projections in Coxeter planes of the E6 Coxeter group, and other subgroups. Symmetric orthographic projections...

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...

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...