# Difference between revisions of "ApCoCoA-1:Oktaeder group"

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− | === <div id="Oktaeder group">[[:ApCoCoA:Symbolic data#Oktaeder_group|Oktaeder | + | === <div id="Oktaeder group">[[:ApCoCoA:Symbolic data#Oktaeder_group|Oktaeder Group]]</div> === |

==== Description ==== | ==== Description ==== | ||

The Oktaeder group is a subgroup of the symmetric group. Like the Tetraeder group this group is generated | The Oktaeder group is a subgroup of the symmetric group. Like the Tetraeder group this group is generated |

## Latest revision as of 20:59, 22 April 2014

#### Description

The Oktaeder group is a subgroup of the symmetric group. Like the Tetraeder group this group is generated only by rotations.

O = <a,b | a^2 = b^3 = (ab)^4 = 1>

#### Reference

Geometries and Transformations, Manuscript, Chapter 11: Finite symmetry groups, N.W. Johnson, 2011

#### Computation

/*Use the ApCoCoA package ncpoly.*/ Use ZZ/(2)[a,b]; NC.SetOrdering("LLEX"); Define CreateRelationsOktaeder() Relations:=[]; // add the relation a^2 = 1 Append(Relations,[[a^2],[1]]); // add the relation b^3 = 1 Append(Relations,[[b^3],[1]]); // add the relation (ab)^4 = 1 Append(Relations,[[a,b,a,b,a,b,a,b],[1]]); Return Relations; EndDefine; Relations:=CreateRelationsOktaeder(); Gb:=NC.GB(Relations);

#### Example in Symbolic Data Format

<FREEALGEBRA createdAt="2014-01-20" createdBy="strohmeier"> <vars>a,b</vars> <basis> <ncpoly>a*a-1</ncpoly> <ncpoly>b*b*b-1</ncpoly> <ncpoly>(a*b)^4-1</ncpoly> </basis> <Comment>Oktaeder_group</Comment> </FREEALGEBRA>