Dihedral Groups #
We define the dihedral groups DihedralGroup n
, with elements r i
and sr i
for i : ZMod n
.
For n ≠ 0
, DihedralGroup n
represents the symmetry group of the regular n
-gon. r i
represents the rotations of the n
-gon by 2πi/n
, and sr i
represents the reflections of the
n
-gon. DihedralGroup 0
corresponds to the infinite dihedral group.
- r: {n : ℕ} → ZMod n → DihedralGroup n
- sr: {n : ℕ} → ZMod n → DihedralGroup n
For n ≠ 0
, DihedralGroup n
represents the symmetry group of the regular n
-gon.
r i
represents the rotations of the n
-gon by 2πi/n
, and sr i
represents the reflections of
the n
-gon. DihedralGroup 0
corresponds to the infinite dihedral group.
Instances For
The group structure on DihedralGroup n
.
If 0 < n
, then DihedralGroup n
is a finite group.
If 0 < n
, then DihedralGroup n
has 2n
elements.
If 0 < n
, then sr i
has order 2.
If 0 < n
, then r 1
has order n
.