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Symmetry group

In group theory, the symmetry group of a geometric object is the group of all transformations under which the object is invariant, endowed with the group operation of composition. Such a transformation is an invertible mapping of the ambient space which takes the object to itself, and which preserves all the relevant structure of the object. A frequent…

Symmetry groups in general, Two dimensions & Introduction

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Overview

Introduction

One dimension

Two dimensions

Three dimensions

Symmetry groups in general

Group structure in terms of symmetries

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Map overview Semantic statistics

Symmetry group

Nodes86
Edges85
Triples81
Avg. degree1.98
Density0.023256
Components1

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Symmetry group

Top relations

related to Further reading · 36
Symmetry group → Academic Press, America, Archived, Boston, Burns, Clegg, Crystal Structure Determination, Crystal Structures, DC, Engineers, Glazer, Hyde, Inc, ISBN, Lock-gray-alt-2, Lock-green, Lock-red-alt-2, Miller, Mineralogical Society, Monograph Series
related to Symmetry groups in general · 11
Symmetry group → Conversely, Each, Erlangen, Escher, Euclidean, For, Fuchsian, In, Just, Similarly, Some
related to Group structure in terms of symmetries · 9
Symmetry group → Add, Cayley's, Euclidean, For, In, Now, Such, Sym, Then
related to External links · 7
Symmetry group → Archived, Eric, MathWorld, Overview, Retrieved, Tetrahedral Group, Weisstein
related to One dimension · 7
Symmetry group → C1the, C2, C2the, Dih, Euclidean, However, The
related to Introduction · 5
Symmetry group → An, For, Sym, The, We
related to Three dimensions · 4
Symmetry group → In, The, This, Up

Important terminology Word statistics

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Important terminology

symmetry group groups point may also figure subgroup example euclidean space object rotations one two structure discrete isometry geometric symmetries

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
arrows or colors to X so as to break all symmetryinstance ofAdd some patterns0.80text
obtaining a figure Xinstance ofAdd some patterns0.80text
Symmetry grouprelated to External linksWeisstein0.60section
Symmetry grouprelated to External linksEric0.60section
Symmetry grouprelated to External linksMathWorld0.60section
Symmetry grouprelated to External linksTetrahedral Group0.60section
Symmetry grouprelated to External linksOverview0.60section
Symmetry grouprelated to External linksArchived0.60section
Symmetry grouprelated to External linksRetrieved0.60section
Symmetry grouprelated to Further readingLock-green0.60section
Symmetry grouprelated to Further readingLock-gray-alt-20.60section
Symmetry grouprelated to Further readingLock-red-alt-20.60section

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