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...

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...

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

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

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...

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

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...

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...

simply laced finite Coxeter groups, by the same diagrams: in this case the Dynkin diagrams exactly coincide with the Coxeter diagrams, as there are no multiple...

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...

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

can be generated by these three Coxeter groups, represented by permutations of rings of the Coxeter-Dynkin diagrams: Selected regular and uniform 9-polytopes...

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...

En Coxeter group, and having only regular polytope facets. The family was named by their Coxeter symbol k21 by its bifurcating Coxeter–Dynkin diagram, with...

There are some exceptional isomorphisms of Dynkin diagrams, yielding isomorphisms of the corresponding Coxeter groups and of polytopes realizing the symmetries...

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

books and papers, F4 is sometimes denoted by E4. The Dynkin diagram for F4 is: . Its Weyl/Coxeter group G = W(F4) is the symmetry group of the 24-cell:...

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...

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...

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...

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...

Symmetry doubled for Ak graphs with even k due to symmetrically-ringed Coxeter-Dynkin diagram. This configuration matrix represents the expanded 6-simplex, with...

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

represented by an empty Schläfli symbol {}, or Coxeter-Dynkin diagram . The dot or node of the Coxeter-Dynkin diagram itself represents a reflection generator...

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...

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...

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