About: Reflection group     Goto   Sponge   NotDistinct   Permalink

An Entity of Type : yago:Group100031264, within Data Space : dbpedia.org associated with source document(s)
QRcode icon
http://dbpedia.org/describe/?url=http%3A%2F%2Fdbpedia.org%2Fresource%2FReflection_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 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.

AttributesValues
rdf:type
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 .
foaf:isPrimaryTopicOf
dct:subject
Wikipage page ID
Wikipage revision ID
Link from a Wikipage to another Wikipage
Link from a Wikipage to an external page
sameAs
dbp:wikiPageUsesTemplate
id
  • Reflection_group
title
  • Reflection group
has abstract
  • 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 .
prov:wasDerivedFrom
page length (characters) of wiki page
is foaf:primaryTopic of
is Link from a Wikipage to another Wikipage of
Faceted Search & Find service v1.17_git51 as of Sep 16 2020


Alternative Linked Data Documents: PivotViewer | iSPARQL | ODE     Content Formats:       RDF       ODATA       Microdata      About   
This material is Open Knowledge   W3C Semantic Web Technology [RDF Data] Valid XHTML + RDFa
OpenLink Virtuoso version 08.03.3319 as of Dec 29 2020, on Linux (x86_64-centos_6-linux-glibc2.12), Single-Server Edition (61 GB total memory)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2021 OpenLink Software