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Point group

In geometry, a point group is a mathematical group of symmetry operations (isometries in a Euclidean space) that have a fixed point in common. The coordinate origin of the Euclidean space is conventionally taken to be a fixed point, and every point group in dimension d is then a subgroup of the orthogonal group O(d). Point groups are used to describe the…

Standards, Overview & Chiral and achiral point groups, reflection groups

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Overview

Chiral and achiral point groups, reflection groups

Two dimensions

Three dimensions

Four dimensions

Seven dimensions

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Point group

Nodes43
Edges42
Triples36
Avg. degree1.95
Density0.046512
Components1

How this topic connects Entity context

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Point group

Top relations

related to Four dimensions · 10
Point group → Conway, Coxeter, Coxeter's, Each, Front-back, Related, Section, Smith, Tables, The
related to Chiral and achiral point groups, reflection groups · 8
Point group → Coxeter, Dynkin, Finite Coxeter, In, Point, Reflection, SO, The
related to External links · 8
Point group → Cartesian Coordinates, Flash, Formulas, Java, Subgroup, Symmetries, The Geometry Center, Web-based
related to Three dimensions · 4
Point group → In Schoenflies, Platonic, Point, They
related to Two dimensions · 2
Point group → Point, They
is a · 1
Point group → mathematical group of symmetry operations
related to One dimension · 1
Point group → There
see also · 1
Point group → Bravais

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Important terminology

groups point coxeter group reflection symmetry chiral represented notation related crystallographic dimensions order space achiral two symmetries example three also

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Point groupis amathematical group of symmetry operations0.90text
molecules.Each point group can be represented as sets of orthogonal matrices M that transform point x into point y according to yinstance ofPoint groups are used to describe the symmetries of geometric figures and physical objects0.80text
Point grouprelated to Chiral and achiral point groups, reflection groupsPoint0.60section
Point grouprelated to Chiral and achiral point groups, reflection groupsThe0.60section
Point grouprelated to Chiral and achiral point groups, reflection groupsSO0.60section
Point grouprelated to Chiral and achiral point groups, reflection groupsIn0.60section
Point grouprelated to Chiral and achiral point groups, reflection groupsFinite Coxeter0.60section
Point grouprelated to Chiral and achiral point groups, reflection groupsCoxeter0.60section
Point grouprelated to Chiral and achiral point groups, reflection groupsDynkin0.60section
Point grouprelated to Chiral and achiral point groups, reflection groupsReflection0.60section
Point grouprelated to External linksWeb-based0.60section
Point grouprelated to External linksJava0.60section

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