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WOLFRAM|DEMONSTRATIONS PROJECT

Dihedral Group of the Square

​
labels
1
2
3
subgroup
1
There are 10 subgroups. This subgroup is not abelian.
set =
{
I
4
,
R
1
,
R
2
,
R
3
,H,
Δ
1
,V,
Δ
2
}
inverse =
{
I
4
,
R
3
,
R
2
,
R
1
,H,
Δ
1
,V,
Δ
2
}
order =
{1,4,2,4,2,2,2,2}
In mathematics, a dihedral group
D
n
is the group of symmetries of a regular polygon with
n
sides, including both rotations and reflections. This Demonstration shows the subgroups of
D
4
, the dihedral group of a square.
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