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GroupTheory

  

RubiksCubeGroup

  

construct a permutation group isomorphic to the group of Rubik's Cube

 

Calling Sequence

Description

Examples

Compatibility

Calling Sequence

RubiksCubeGroup()

Description

• 

The group of Rubik's Cube (TM) is a group of cube transformations of the popular Rubik's Cube (TM) puzzle game.

• 

The RubiksCubeGroup() command returns a permutation group isomorphic to the Rubik's Cube (TM) group.

Examples

withGroupTheory:

RRubiksCubeGroup

R < a permutation group on 48 letters with 6 generators >

(1)

GroupOrderR

43252003274489856000

(2)

DegreeR

48

(3)

IsTransitiveR

false

(4)

numelemsOrbitsR

2

(5)

mapnumelems&comma;OrbitsR

24&comma;24

(6)

LabelsR

front&comma;back&comma;left&comma;right&comma;up&comma;down

(7)

zipassign&comma;LabelsR&comma;GeneratorsR&colon;

Let us construct the so-called "slice squared" subgroup, whose generators rotate a central "slice" by a half-turn.

SSSubgroupfront2·back2&comma;right2·left2&comma;up2·down2&comma;R

SS1&comma;482&comma;473&comma;466&comma;437&comma;428&comma;419&comma;3211&comma;3012&comma;2913&comma;2814&comma;2716&comma;2517&comma;2418&comma;2319&comma;2220&comma;2133&comma;4034&comma;3935&comma;3836&comma;37&comma;1&comma;413&comma;434&comma;445&comma;456&comma;468&comma;489&comma;1610&comma;1511&comma;1412&comma;1317&comma;4019&comma;3820&comma;3721&comma;3622&comma;3524&comma;3325&comma;3226&comma;3127&comma;3028&comma;29&comma;1&comma;82&comma;73&comma;64&comma;59&comma;2510&comma;2611&comma;2714&comma;3015&comma;3116&comma;3217&comma;3318&comma;3419&comma;3522&comma;3823&comma;3924&comma;4041&comma;4842&comma;4743&comma;4644&comma;45

(8)

These generators commute with one another, so they generate a commutative subgroup of R.

IsAbelianSS

true

(9)

GroupOrderSS

8

(10)

Compatibility

• 

The GroupTheory[RubiksCubeGroup] command was introduced in Maple 17.

• 

For more information on Maple 17 changes, see Updates in Maple 17.

See Also

GroupTheory[Degree]

GroupTheory[GroupOrder]

GroupTheory[IsAbelian]

GroupTheory[IsTransitive]

GroupTheory[Subgroup]