Category:Dihedral Group D3

This category contains results about Dihedral Group D3.

Let $\triangle ABC$ be an equilateral triangle.

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

$\ds e$

$:$

$\ds \tuple A \tuple B \tuple C$

$\ds p$

$:$

$\ds \tuple {ABC}$

$\ds q$

$:$

$\ds \tuple {ACB}$

Rotation of $120 \degrees$ clockwise about center

$\ds r$

$:$

$\ds \tuple {BC}$

$\ds s$

$:$

$\ds \tuple {AC}$

$\ds t$

$:$

$\ds \tuple {AB}$

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.

Pages in category "Dihedral Group D3"

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