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

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...

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

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

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

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...

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...

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...

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...

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

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...

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...

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...

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

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

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 231, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of the 2-node...

order-3 dihedral angles. They can be seen as one-end-ringed Coxeter–Dynkin diagrams. The Coxeter symbol for these figures has the form ki,j, where each letter...

{\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...

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

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...

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

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...

symmetry can be generated by these four Coxeter groups, represented by permutations of rings of the Coxeter-Dynkin diagrams: The A7 family has symmetry of order...

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...

cocompact groups where removing any permutation of two nodes in its Coxeter–Dynkin diagram leaves a finite or Euclidean graph. The tenth dimension is the highest...

can be generated by these three Coxeter groups, represented by permutations of rings of the Coxeter-Dynkin diagrams: Selected regular and uniform 10-polytopes...

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...

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...