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GroupTheory

  

DihedralGroup

  

construct a dihedral group of a given degree

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

DihedralGroup( n )

DihedralGroup( n, s )

Parameters

n

-

a positive integer

s

-

optional equation: form="fpgroup" or form="permgroup" (the default)

Description

• 

The dihedral group of degree n is the symmetry group of an n-sided regular polygon for 1<n.  It is generated by a reflection (of order 2), and a rotation (of order n).  It acts as a permutation group on the vertices of the regular n-sided polygon.

• 

The DihedralGroup( n ) command returns a dihedral group, either as a permutation group or a group defined by generators and defining relations. By default, a permutation group is returned, but a finitely presented group can be requested by passing the option 'form' = "fpgroup".

• 

If the value of the parameter n is not numeric, then a symbolic group representing the dihedral group of the indicated degree is returned.

Examples

withGroupTheory&colon;

DihedralGroup13

D13

(1)

DihedralGroup13&comma;form&equals;fpgroup

D13

(2)

DihedralGroup13&comma;form&equals;permgroup

D13

(3)

GroupOrderDihedralGroup3k

6k

(4)

IsNilpotentDihedralGroup6kassumingk::posint

false

(5)

Compatibility

• 

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

• 

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

See Also

GroupTheory[DicyclicGroup]

GroupTheory[GroupOrder]

GroupTheory[IsNilpotent]

 


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