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- Coxeter_group abstract "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 mirrors). Indeed, the finite Coxeter groups are precisely the finite Euclidean reflection groups; the symmetry groups of regular polyhedra are an example. However, not all Coxeter groups are finite, and not all can be described in terms of symmetries and Euclidean reflections. Coxeter groups were introduced (Coxeter 1934) as abstractions of reflection groups, and finite Coxeter groups were classified in 1935 (Coxeter 1935).Coxeter groups find applications in many areas of mathematics. Examples of finite Coxeter groups include the symmetry groups of regular polytopes, and the Weyl groups of simple Lie algebras. Examples of infinite Coxeter groups include the triangle groups corresponding to regular tessellations of the Euclidean plane and the hyperbolic plane, and the Weyl groups of infinite-dimensional Kac–Moody algebras.Standard references include (Humphreys 1990) and (Davis 2007).".
- Coxeter_group wikiPageExternalLink books?id=1TBPz5sd8m0C.
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- Coxeter_group wikiPageExternalLink 6049.
- Coxeter_group wikiPageExternalLink jfs110203.pdf.
- Coxeter_group wikiPageExternalLink davisbook.pdf.
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- Coxeter_group wikiPageLength "27823".
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- Coxeter_group wikiPageRevisionID "648200549".
- Coxeter_group wikiPageWikiLink 120-cell.
- Coxeter_group wikiPageWikiLink 16-cell_honeycomb.
- Coxeter_group wikiPageWikiLink 1_22_polytope.
- Coxeter_group wikiPageWikiLink 1_32_polytope.
- Coxeter_group wikiPageWikiLink 1_33_honeycomb.
- Coxeter_group wikiPageWikiLink 1_42_polytope.
- Coxeter_group wikiPageWikiLink 1_52_honeycomb.
- Coxeter_group wikiPageWikiLink 24-cell.
- Coxeter_group wikiPageWikiLink 24-cell_honeycomb.
- Coxeter_group wikiPageWikiLink 2_21_polytope.
- Coxeter_group wikiPageWikiLink 2_22_honeycomb.
- Coxeter_group wikiPageWikiLink 2_31_polytope.
- Coxeter_group wikiPageWikiLink 2_41_polytope.
- Coxeter_group wikiPageWikiLink 2_51_honeycomb.
- Coxeter_group wikiPageWikiLink 3_21_polytope.
- Coxeter_group wikiPageWikiLink 3_31_honeycomb.
- Coxeter_group wikiPageWikiLink 4_21_polytope.
- Coxeter_group wikiPageWikiLink 5_21_honeycomb.
- Coxeter_group wikiPageWikiLink 600-cell.
- Coxeter_group wikiPageWikiLink Abelian_group.
- Coxeter_group wikiPageWikiLink Abelianization.
- Coxeter_group wikiPageWikiLink Alternated_hypercubic_honeycomb.
- Coxeter_group wikiPageWikiLink Apeirogon.
- Coxeter_group wikiPageWikiLink Artin_group.
- Coxeter_group wikiPageWikiLink Automatic_group.
- Coxeter_group wikiPageWikiLink Bruhat_order.
- Coxeter_group wikiPageWikiLink Category:Coxeter_groups.
- Coxeter_group wikiPageWikiLink Cayley_graph.
- Coxeter_group wikiPageWikiLink Chevalley–Shephard–Todd_theorem.
- Coxeter_group wikiPageWikiLink Commutative_operation.
- Coxeter_group wikiPageWikiLink Commutative_property.
- Coxeter_group wikiPageWikiLink Commutator.
- Coxeter_group wikiPageWikiLink Commutator_subgroup.
- Coxeter_group wikiPageWikiLink Complex_reflection_group.
- Coxeter_group wikiPageWikiLink Conjugate_element_(field_theory).
- Coxeter_group wikiPageWikiLink Conjugate_elements.
- Coxeter_group wikiPageWikiLink Connected_component_(graph_theory).
- Coxeter_group wikiPageWikiLink Coxeter-Dynkin_diagram.
- Coxeter_group wikiPageWikiLink Coxeter_diagram.
- Coxeter_group wikiPageWikiLink Coxeter_element.
- Coxeter_group wikiPageWikiLink Coxeter_notation.
- Coxeter_group wikiPageWikiLink Coxeter_number.
- Coxeter_group wikiPageWikiLink Coxeter–Dynkin_diagram.
- Coxeter_group wikiPageWikiLink Cross-polytope.
- Coxeter_group wikiPageWikiLink Crystallographic_restriction_theorem.
- Coxeter_group wikiPageWikiLink Cube.
- Coxeter_group wikiPageWikiLink Cyclic_group.
- Coxeter_group wikiPageWikiLink Cyclic_permutation.
- Coxeter_group wikiPageWikiLink Demihypercube.
- Coxeter_group wikiPageWikiLink Demihypercubic_honeycomb.
- Coxeter_group wikiPageWikiLink Dihedral_group.
- Coxeter_group wikiPageWikiLink Direct_product_of_groups.
- Coxeter_group wikiPageWikiLink Disjoint_union.
- Coxeter_group wikiPageWikiLink Dodecahedron.
- Coxeter_group wikiPageWikiLink Dot_product.
- Coxeter_group wikiPageWikiLink Dual_polyhedron.
- Coxeter_group wikiPageWikiLink Dual_polytope.
- Coxeter_group wikiPageWikiLink Dynkin_diagram.
- Coxeter_group wikiPageWikiLink E6_(mathematics).
- Coxeter_group wikiPageWikiLink E7_(mathematics).
- Coxeter_group wikiPageWikiLink E8_(mathematics).
- Coxeter_group wikiPageWikiLink Edge_(graph_theory).
- Coxeter_group wikiPageWikiLink Eigenvalues.
- Coxeter_group wikiPageWikiLink Eigenvalues_and_eigenvectors.
- Coxeter_group wikiPageWikiLink Elementary_abelian_group.
- Coxeter_group wikiPageWikiLink Ernst_Witt.
- Coxeter_group wikiPageWikiLink Euclidean_plane.
- Coxeter_group wikiPageWikiLink Exceptional_object.
- Coxeter_group wikiPageWikiLink F4_(mathematics).
- Coxeter_group wikiPageWikiLink François_Bruhat.
- Coxeter_group wikiPageWikiLink Full_icosahedral_group.
- Coxeter_group wikiPageWikiLink G2_(mathematics).
- Coxeter_group wikiPageWikiLink Generating_set_of_a_group.
- Coxeter_group wikiPageWikiLink Graded_poset.
- Coxeter_group wikiPageWikiLink Graduate_Texts_in_Mathematics.
- Coxeter_group wikiPageWikiLink Graph_(mathematics).
- Coxeter_group wikiPageWikiLink Group_(mathematics).
- Coxeter_group wikiPageWikiLink Group_algebra.
- Coxeter_group wikiPageWikiLink Group_cohomology.
- Coxeter_group wikiPageWikiLink Group_homology.
- Coxeter_group wikiPageWikiLink Group_presentation.
- Coxeter_group wikiPageWikiLink Harold_Scott_MacDonald_Coxeter.
- Coxeter_group wikiPageWikiLink Hasse_diagram.
- Coxeter_group wikiPageWikiLink Hecke_algebra.
- Coxeter_group wikiPageWikiLink Hexagon.
- Coxeter_group wikiPageWikiLink Hexagonal_tiling.