# 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 symmetries on $\triangle ABC$:

\(\ds e\) | \(:\) | \(\ds \tuple A \tuple B \tuple C\) | Identity mapping | |||||||||||

\(\ds p\) | \(:\) | \(\ds \tuple {ABC}\) | Rotation of $120 \degrees$ anticlockwise about center | |||||||||||

\(\ds q\) | \(:\) | \(\ds \tuple {ACB}\) | Rotation of $120 \degrees$ clockwise about center | |||||||||||

\(\ds r\) | \(:\) | \(\ds \tuple {BC}\) | Reflection in line $r$ | |||||||||||

\(\ds s\) | \(:\) | \(\ds \tuple {AC}\) | Reflection in line $s$ | |||||||||||

\(\ds t\) | \(:\) | \(\ds \tuple {AB}\) | 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 7 pages are in this category, out of 7 total.