TITLE: Calculate coordinates of a regular polygon
QUESTION [7 upvotes]: Given the regular polygon's side count $n$, the circumscribed radius $r$ and the center coordinates $(x,y)$ of the circumscribed circle,
How to calculate the coordinates of all polygon's vertices if one of the vertices coordinates are $(x,?)$?

REPLY [4 votes]: Supposing you know complex numbers, we care only about polygons around the origin which are inscribed in the unit circle. If a vertex is at $e^{i\omega}$, then the other n vertices will be at $e^{i(\omega + 2\pi k/n)}$ for $k$ up to $n$.
Then, if they're not on the unit circle, multiply everything by the radius.
If it's not centered at the origin, translate it to that spot instead.