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Statements

Subject Item
dbr:Reflection_group
rdf:type
yago:WikicatReflectionGroups yago:Group100031264 yago:Abstraction100002137 dbo:Band
rdfs:label
Reflection group Gruppo di riflessione Grupa odbić
rdfs:comment
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 crystallographic Coxeter groups. While the orthogonal group is generated by reflections (by the Cartan–Dieudonné theorem), it is a continuous group (indeed, Lie group), not a discrete group, and is generally considered separately. Un gruppo di riflessione, in geometria e nella teoria dei gruppi, è un gruppo discreto generato dall'insieme delle riflessioni di uno spazio euclideo di dimensione finita. Tra i gruppi di riflessione si annoverano anche i gruppi di Weyl e i gruppi cristallografici di Coxeter. Grupa odbić – dyskretna grupa odwzorowań generowana przez symetrie względem hiperpowierzchni przestrzeni euklidesowej lub przestrzeni hiperbolicznej lub innej jednospójnej przestrzeni Riemanna o stałej .
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Reflection_group
dbp:title
Reflection group
dbo:abstract
Grupa odbić – dyskretna grupa odwzorowań generowana przez symetrie względem hiperpowierzchni przestrzeni euklidesowej lub przestrzeni hiperbolicznej lub innej jednospójnej przestrzeni Riemanna o stałej . 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 crystallographic Coxeter groups. While the orthogonal group is generated by reflections (by the Cartan–Dieudonné theorem), it is a continuous group (indeed, Lie group), not a discrete group, and is generally considered separately. Un gruppo di riflessione, in geometria e nella teoria dei gruppi, è un gruppo discreto generato dall'insieme delle riflessioni di uno spazio euclideo di dimensione finita. Tra i gruppi di riflessione si annoverano anche i gruppi di Weyl e i gruppi cristallografici di Coxeter.
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