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

(undirected) Dynkin diagrams with the restrictions on Coxeter diagrams of finite groups: formally, the Coxeter graph can be obtained from the Dynkin diagram by...

a Dynkin diagram, named for Eugene Dynkin, is a type of graph with some edges doubled or tripled (drawn as a double or triple line). Dynkin diagrams arise...

Aleksandr Dynkin (born 1948), Russian economist Eugene Dynkin (1924–2014), Soviet and American mathematician known for Dynkin diagram Coxeter–Dynkin diagram Dynkin...

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

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 of the 4-node...

named as V72 (for its 72 vertices). Its Coxeter symbol is 122, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of the 1-node...

Algebra Affine Dynkin diagram Coxeter–Dynkin diagram Dynkin index Dynkin–Specht–Wever Lemma Probability Dynkin's card trick Dynkin's formula Dynkin system Vvedenskaya...

(nonconvex regular polyhedra), with Schläfli symbol {3,5⁄2} and Coxeter-Dynkin diagram of . It is composed of 20 intersecting triangular faces, having...

also called the Schläfli polytope. Its Coxeter symbol is 221, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of one of...

group) are accordingly finite Coxeter groups, which allows them to be classified by their Coxeter–Dynkin diagram. Being a Coxeter group means that a Weyl group...

polytope, constructed from the E7 group. Its Coxeter symbol is 132, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of one of...

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

symmetry can be generated by these four Coxeter groups, represented by permutations of rings of the Coxeter-Dynkin diagrams: Selected regular and uniform 8-polytopes...

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

poset. ADE classification Affine root system Coxeter–Dynkin diagram Coxeter group Coxeter matrix Dynkin diagram root datum Semisimple Lie algebra Weights...

permutations of rings of the Coxeter-Dynkin diagrams. Each combination of at least one ring on every connected group of nodes in the diagram produces a uniform...

polytope, constructed from the E7 group. Its Coxeter symbol is 231, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of the 2-node...

of Coxeter groups with a bifurcated Coxeter-Dynkin diagram of lengths 6,2,1. There are 1023 unique E10 honeycombs by all combinations of its Coxeter-Dynkin...

q}. The Coxeter-Dynkin diagram is a triangular graph with p, q, r labeled on the edges. If r = 2, then the graph is linear, since diagram nodes with...

Coxeter-Dynkin diagram The icosidodecahedron { 3 5 } {\displaystyle {\begin{Bmatrix}3\\5\end{Bmatrix}}} , vertex configuration (3.5)2, Coxeter-Dynkin...

within the symmetry of the E8 group. Its Coxeter symbol is 142, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of the 1-node...

called it an 7-ic semi-regular figure. Its Coxeter symbol is 321, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of one of...

that creates a maximum number of facets. It is represented in a Coxeter–Dynkin diagram with all nodes ringed. It is a shortcut term which has a different...

Euclidean space. The symbol 521 is from Coxeter, named for the length of the 3 branches of its Coxeter-Dynkin diagram. By putting spheres at its vertices...

15=14400.\end{aligned}}} Distinct Coxeter elements correspond to orientations of the Coxeter diagram (i.e. to Dynkin quivers): the simple reflections corresponding...

within the symmetry of the E8 group. Its Coxeter symbol is 241, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of the 2-node...

the structure of a Coxeter-Dynkin diagram, with modifiers to indicate certain subgroups. The notation is named after H. S. M. Coxeter, and has been more...

polytope. Regular polytopes are in bijection with Coxeter groups with linear Coxeter-Dynkin diagram (without branch point) and an increasing numbering...

and 6 vertices. Its vertex figure is a crossed quadrilateral. Its Coxeter–Dynkin diagram is (although this is a double covering of the tetrahemihexahedron)...