Sorry for my naivety I am trying to plot the points of n sided regular polygons but maintaining the height between odd and even sided polygons.
Is there a sensible algorithm for doing so before I venture forward with a naive one?
Hopefully something visual will help elucidate the problem: https://youtu.be/OXVZjDUAA4c
The height of an $n$-gon (with $n$ odd) is $$ \left(1+\cos\left(\frac{\pi}{n}\right)\right)\cdot r. $$ The height of an $n$-gon (with $n$-even) is $$ 2r. $$ So you can get the same height by scaling the size appropriatly.