The general formula for vertices of a regular polygon in polar coordintates is

(r,w_i) = (r, offset+2*pi*i/n), where i = 0, 1, ..., n-1
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with r the radius and offset the orientation. This polygon will fit inside a circle of radius r, or a 2r by 2r square.

In rectangular coords, that is

x_i = r * cos(w_i)   y_i = r * sin(w_i)
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