Coset/Examples/Symmetry Group of Equilateral Triangle/Cosets of Reflection Subgroup

Examples of Cosets
Consider the symmetry group of the equilateral triangle $D_3$.


 * SymmetryGroupEqTriangle.png

Let $H \subseteq D_3$ be defined as:
 * $H = \set {e, r}$

where:
 * $e$ denotes the identity mapping
 * $r$ denotes reflection in the line $r$.

The left cosets of $H$ are:

The right cosets of $H$ are: