Dihedral Group/Group Presentation

Theorem
The dihedral group $D_n$ is generated by two elements $\alpha$ and $\beta$ such that:
 * $(1): \quad \alpha^n = e$
 * $(2): \quad \beta^2 = e$
 * $(3): \quad \beta \alpha = \alpha^{n-1} \beta$

Proof
Let $\alpha$ be rotation by $\frac{2 \pi}{n}$.

Let $\beta$ be reflection across the y axis.