Coxeter–Dynkin diagram

<p>In <a href="/facts/Geometry/wTQf5ffQ">geometry</a>, a <a href="/facts/Harold_Scott_MacDonald_Coxeter/D2l5jWGG">Coxeter</a>–<a href="/facts/Eugene_Dynkin/RMIBmG9q">Dynkin</a> diagram (or Coxeter diagram, Coxeter graph) is a <a href="/facts/Graph_(discrete_mathematics)/kw3eIBUe">graph</a> with numerically labeled edges (called branches) representing a <a href="/facts/Coxeter_group/bgzHFm1Q">Coxeter group</a> or sometimes a <a href="/facts/Uniform_polytope/nFcNAzLy">uniform polytope</a> or <a href="/facts/Uniform_tiling/QVK02ksI">uniform tiling</a> constructed from the group.
</p><p>A class of closely related objects is the <a href="/facts/Dynkin_diagram/oBhUwRIR">Dynkin diagrams</a>, which differ from Coxeter diagrams in two respects: firstly, branches labeled "4" or greater are <a href="/facts/Directed_graph/YBdfQ0um">directed</a>, while Coxeter diagrams are <a href="/facts/Undirected_graph/kw3eIBUe">undirected</a>; secondly, Dynkin diagrams must satisfy an additional (<a href="/facts/Crystallographic_restriction_theorem/tojdCRI8">crystallographic</a>) restriction, namely that the only allowed branch labels are 2, 3, 4, and 6. Dynkin diagrams correspond to and are used to classify <a href="/facts/Root_system/TFaEdwMU">root systems</a> and therefore <a href="/facts/Semisimple_Lie_algebra/m8jA3Bcf">semisimple Lie algebras</a>.
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Coxeter–Dynkin diagram open-in-new

Coxeter–Dynkin diagram