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Point groups in three dimensions

In geometry, a point group in three dimensions is an isometry group in three dimensions that leaves the origin fixed, or correspondingly, an isometry group of a sphere. It is a subgroup of the orthogonal group O(3), the group of all isometries that leave the origin fixed, or correspondingly, the group of orthogonal matrices. O(3) itself is a subgroup of…

Standards, The seven infinite series of axial groups & Binary polyhedral groups

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Overview

3D isometries that leave the origin fixed

Conjugacy

Infinite isometry groups

Finite isometry groups

The seven infinite series of axial groups

The seven remaining point groups

Reflective Coxeter groups

Rotation groups

Correspondence between rotation groups and other groups

The groups arranged by abstract group type

Fundamental domain

Binary polyhedral groups

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Point groups in three dimensions

Nodes142
Edges141
Triples8
Avg. degree1.99
Density0.014085
Components1

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Point groups in three dimensions

Top relations

related to Reflective Coxeter groups · 7
Point groups in three dimensions → Cnv, Coxeter, Coxeter-Dynkin, Dnh, In Coxeter, In Schoenflies, The

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Important terminology

group groups symmetry rotation also point axis plane reflection cn order two notation infinite rotations 3d origin generated isometry called

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Concanavalin Ainstance ofD2 occurs in molecules such as twistane and in homotetramers0.80text
Point groups in three dimensionsrelated to Reflective Coxeter groupsThe0.60section
Point groups in three dimensionsrelated to Reflective Coxeter groupsCoxeter0.60section
Point groups in three dimensionsrelated to Reflective Coxeter groupsCoxeter-Dynkin0.60section
Point groups in three dimensionsrelated to Reflective Coxeter groupsIn Schoenflies0.60section
Point groups in three dimensionsrelated to Reflective Coxeter groupsCnv0.60section
Point groups in three dimensionsrelated to Reflective Coxeter groupsDnh0.60section
Point groups in three dimensionsrelated to Reflective Coxeter groupsIn Coxeter0.60section

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