I'm trying to find the formula for the vertices of a polygon with n-sides such that there is always only 1 vertex at the top and the polygon is symmetric with respect to the y-axis...
so generally the formula for the vertices of a polygon is
$$ x_i = r \cos \Big ( \psi + \frac{ 2 \pi i }{n}\Big ) $$
and
$$ y_i = r \sin \Big ( \psi + \frac{ 2 \pi i }{n}\Big ) $$
where $(x_i,y_i)$ is the $i$th vertex of a polygon of $n$-sides and $r$ is the radius, and $\psi$ is the angle by which the polygon is rotated.
So the question is to find the function $\psi$. I would assume $\psi$ is a function of $i$ and $n$
I've tried a few examples but can't seem to find a general formula for $\psi(i,n)$
so for the example of the triangle we want this: