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Reflection group

In group theory and geometry, a reflection group is a discrete group which is generated by a set of reflections of a finite-dimensional Euclidean space. The symmetry group of a regular polytope or of a tiling of the Euclidean space by congruent copies of a regular polytope is necessarily a reflection group. Reflection groups also include Weyl groups and…

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Relation with Coxeter groups

Finite fields

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Reflection group

Nodes45
Edges44
Triples51
Avg. degree1.96
Density0.044444
Components1

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Reflection group

Top relations

related to Generalizations · 8
Reflection group → Discrete, Euclidean, Hn, In, Riemannian, Rn, Sn, The
related to Three dimensions · 8
Reflection group → ADE, Cnv, Dnh, Dual, Finite, Platonic, R3, The
related to External links · 7
Reflection group → EMS Press, Encyclopedia, Mathematics, Media, Reflection, Wikimedia Commons, Wiktionary-logo-en-v2
related to Relation with Coxeter groups · 6
Reflection group → All, Coxeter, Hi, Hj, The, Thus
related to Finite fields · 5
Reflection group → Geometrically, Reflection, Serežkin, When, Zalesskiĭ
related to Two dimensions · 5
Reflection group → Conversely, Coxeter, If, In, Infinite
is a · 4
Reflection group → Coxeter group, discrete group which is generated by a set of reflections of a finite-dimensional Euclidean space, discrete subgroup of the affine group of E that is generated by a set of affine reflections of E, subgroup of the general linear group of E which is generated by a set of orthogonal reflections across hyperplanes passing through the origin
related to Definition · 4
Reflection group → An, Euclidean, Let, The
see also · 4
Reflection group → Hyperplane, Parabolic, Shephard, Todd

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Important terminology

reflection groups reflections group generated finite two coxeter discrete euclidean space fields dimensions also displaystyle set symmetry include subgroup hyperplanes

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Reflection groupis adiscrete group which is generated by a set of reflections of a finite-dimensional Euclidean space0.90text
Reflection groupis asubgroup of the general linear group of E which is generated by a set of orthogonal reflections across hyperplanes passing through the origin0.90text
Reflection groupis adiscrete subgroup of the affine group of E that is generated by a set of affine reflections of E0.90text
Reflection groupis aCoxeter group0.90text
Reflection grouprelated to DefinitionLet0.60section
Reflection grouprelated to DefinitionEuclidean0.60section
Reflection grouprelated to DefinitionAn0.60section
Reflection grouprelated to DefinitionThe0.60section
Reflection grouprelated to External linksWiktionary-logo-en-v20.60section
Reflection grouprelated to External linksMedia0.60section
Reflection grouprelated to External linksReflection0.60section
Reflection grouprelated to External linksWikimedia Commons0.60section

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