# Category:Dihedral Group D3

This category contains examples of Dihedral Group D3.

The dihedral group $D_3$ is the symmetry group of the equilateral triangle:

Let $\triangle ABC$ be an equilateral triangle.

We define in cycle notation the following symmetry mappings on $\triangle ABC$:

 $\displaystyle e$ $:$ $\displaystyle \tuple A \tuple B \tuple C$ Identity mapping $\displaystyle p$ $:$ $\displaystyle \tuple {ABC}$ Rotation of $120 \degrees$ anticlockwise about center $\displaystyle q$ $:$ $\displaystyle \tuple {ACB}$ Rotation of $120 \degrees$ clockwise about center $\displaystyle r$ $:$ $\displaystyle \tuple {BC}$ Reflection in line $r$ $\displaystyle s$ $:$ $\displaystyle \tuple {AC}$ Reflection in line $s$ $\displaystyle t$ $:$ $\displaystyle \tuple {AB}$ Reflection in line $t$

Note that $r, s, t$ can equally well be considered as a rotation of $180 \degrees$ (in $3$ dimensions) about the axes $r, s, t$.

Then these six operations form a group.

This group is known as the symmetry group of the equilateral triangle.

## Pages in category "Dihedral Group D3"

The following 8 pages are in this category, out of 8 total.