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...

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...

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...

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...

or 5-orthoplex. 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...

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

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...

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

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

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...

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

from the B5 Coxeter plane, including the regular 5-cube and 5-orthoplex. Coxeter, Regular Polytopes, sec 1.8 Configurations Coxeter, Complex Regular Polytopes...

space - ScienceDirect". Coxeter, Regular Polytopes, sec 1.8 Configurations Coxeter, Complex Regular Polytopes, p.117 Coxeter, H.S.M. Regular Polytopes...

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

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

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...

have orthographic projections in the H 3 {\displaystyle \mathrm {H} _{3}} Coxeter plane that contain various decagrammic symmetries, which include compound...

The Boerdijk–Coxeter helix, named after H. S. M. Coxeter and Arie Hendrick Boerdijk [es], is a linear stacking of regular tetrahedra, arranged so that...

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

In mathematics, the Coxeter–Todd lattice K12, discovered by Coxeter and Todd (1953), is a 12-dimensional even integral lattice of discriminant 36 with...

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

complex geometry is the study of geometric structures and constructions arising out of, or described by, the complex numbers. In particular, complex geometry...

He called it an 8-ic semi-regular figure. Its Coxeter symbol is 421, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the end...

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

classified by their isometry group. These are finite Coxeter groups, but not every finite Coxeter groups may be realised as the isometry group of a regular...