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

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

a building Δ is a Coxeter group W, which determines a highly symmetrical simplicial complex Σ = Σ(W,S), called the Coxeter complex. A building Δ is glued...

the Coxeter graph, Coxeter groups, Coxeter's loxodromic sequence of tangent circles, Coxeter–Dynkin diagrams, and the Todd–Coxeter algorithm. Coxeter was...

symbolic notation developed by Coxeter. Some complex polytopes which are not fully regular have also been described. The complex line C 1 {\displaystyle \mathbb...

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...

or 5-orthoplex. Coxeter, Regular Polytopes, sec 1.8 Configurations Coxeter, Complex Regular Polytopes, p. 117 H.S.M. Coxeter: Coxeter, Regular Polytopes...

Coxeter 1973, § 1.8 Configurations Coxeter, Complex Regular Polytopes, p.117 Conway, Burgiel & Goodman-Strauss 2008, p. 406, Fig 26.2 Coxeter, Star...

regular complex polygons have been completely characterized, and can be described using a symbolic notation developed by Coxeter. A regular complex polygon...

number of faces in the Coxeter complex associated with a Coxeter group of type A n − 1 {\displaystyle A_{n-1}} . Here, a Coxeter group can be thought of...

1016/S0747-7171(88)80010-5. Coxeter, Regular Polytopes, sec 1.8 Configurations Coxeter, Complex Regular Polytopes, p.117 Coxeter, H.S.M. Regular Polytopes...

with -1 < xi < 1. Coxeter, Regular Polytopes, sec 1.8 Configurations Coxeter, Complex Regular Polytopes, p.117 H.S.M. Coxeter: Coxeter, Regular Polytopes...

real reflection groups (the Coxeter groups or Weyl groups, including the symmetry groups of regular polyhedra). A (complex) reflection r (sometimes also...

dimensional, locally finite, ranked simplicial complex to capture isomorphisms between finite rank Coxeter systems) and asked more related open questions...

Polytopes, sec 1.8 Configurations Coxeter, Complex Regular Polytopes, p.117 H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New...

previous property. Every Coxeter complex, and more generally every building (in the sense of Tits), is shellable. The boundary complex of a (convex) polytope...

complex reflection group, so the complex reflection groups form another generalization of finite real reflection groups. Suppose that W is a Coxeter group...

8th in an infinite series of hypercube: Coxeter, Regular Polytopes, sec 1.8 Configurations Coxeter, Complex Regular Polytopes, p.117 Klitzing, Richard...

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

5-demicube). In Coxeter's notation the 5-demicube is given the symbol 121. Coxeter, Regular Polytopes, sec 1.8 Configurations Coxeter, Complex Regular Polytopes...

the Coxeter complexes that make them up are colorable. A coloring of a building is associated with a uniform choice of Weyl group for the Coxeter complexes...

1016/0012-365X(82)90185-6, MR 0676709 Coxeter 1973, p. 12, §1.8 Configurations. Coxeter 1973, p. 293. Coxeter, H. S. M., Regular Complex Polytopes, second edition...

In 4-dimensional complex geometry, the Witting polytope is a regular complex polytope, named as: 3{3}3{3}3{3}3, and Coxeter diagram . It has 240 vertices...

generalised the idea as complex polytopes in complex space, where each real dimension has an imaginary one associated with it. Coxeter developed the theory...

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 are...

meshes:Surface (polygonal) Simplification 1997. (retrieved May 2016) Coxeter, H. S. M., Regular Complex Polytopes, Cambridge University Press, 1974. Introduction...

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

quasiregular form. Coxeter, Complex Regular polytopes, p.123 Coxeter Regular Convex Polytopes, 12.5 The Witting polytope Coxeter, Complex Regular polytopes...

Dynkin diagrams exactly coincide with Coxeter diagrams, as there are no multiple edges. Dynkin diagrams classify complex semisimple Lie algebras. Real semisimple...

vertices) Coxeter, Regular Polytopes, sec 1.8 Configurations Coxeter, Complex Regular Polytopes, p.117 Klitzing, Richard. "o3x3o3o3o - rix". Coxeter, Regular...