Draw the triangle pointing right such that the rightmost vertex is at $\mathbf{i}$
The coordinates of a regular $n$-gon with a centred on the origin with a vertex at $(1,0)$ are
$$\left(\cos\left(\frac{2m\pi}{n}\right), \sin\left(\frac{2m\pi}{n}\right)\right)\, \text{ where }m=0, \dots, n-1$$
$$(1, 0), \left(\frac{1}{4}\left(\sqrt{5}-1\right), \frac{1}{4}\left(\sqrt{10+2\sqrt{5}}\right)\right), \left(-\frac{1}{4}\left(\sqrt{5}+1\right), \frac{1}{4}\left(\sqrt{10-2\sqrt{5}}\right)\right)$$
along with the mirror images in the $x$-axis.