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

enter image description here

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    $\begingroup$ What do you mean by the "height" of a polygon? $\endgroup$ – user Apr 22 at 19:43
  • $\begingroup$ I guess I mean the radius/ diameter but on closer inspection perhaps that is folly. I will add an image for clarity $\endgroup$ – SacredGeometry Apr 22 at 20:00
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    $\begingroup$ I assume you want all of them inscribed in a circle of a given radius. If this is the case, you simply divide circle into $n$ sectors and your vertices will be on the circle. $\endgroup$ – Vasya Apr 22 at 21:04
  • $\begingroup$ I thought that that is what I was doing when I calculate the x and y pos like this Sorry for the notation format (software engineer not mathematician): x = sin(theta) * radius y = cos(theta) * radius $\endgroup$ – SacredGeometry Apr 22 at 21:12
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    $\begingroup$ With $\theta =2\pi k/n $? $\endgroup$ – user Apr 22 at 21:24

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.

  • $\begingroup$ Thats the one. Thank you so much for your help. $\endgroup$ – SacredGeometry Apr 22 at 22:12

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