# Category:Symmetry Group of Equilateral Triangle

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This category contains results about Symmetry Group of 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 "Symmetry Group of Equilateral Triangle"

The following 5 pages are in this category, out of 5 total.