construct a dihedral group of a given degree
DihedralGroup( n )
DihedralGroup( n, s )
a positive integer
(optional) equation of the form form = "fpgroup" or form = "permgroup" (default)
The dihedral group of degree n is the symmetry group of an n-sided regular polygon for n>2. 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.
For n=1, the dihedral group is a cyclic group of order 2. For n=2, the dihedral group is the non-cyclic group of order 4, also known as the Klein 4-group.
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.
In the Standard Worksheet interface, you can insert this group into a document or worksheet by using the Group Constructors palette.
The GroupTheory[DihedralGroup] command was introduced in Maple 17.
For more information on Maple 17 changes, see Updates in Maple 17.
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