# Solving for semi-regular polygons

Hello!

I am trying to create geometry for CNC milling with grasshopper but I am having some trouble solving for one of the variables in my problem. I have a PVC sculpture that uses various sizes of pipe tensioned together into a larger column, but it needs internal structure to keep it from collapsing onto itself (see images). I made a piece for my mock up, which was small enough to trace onto a piece of wood (also in images), but due to the size and weight of the full sculpture it will not be possible to get an accurate profile from the original.

I know the lengths of all of the PVC pieces and their sequence on the column, so I thought I could translate the overall length into a circumference onto which I could map the PVC and get the internal geometry. The issue is that the length of the chord (the PVC width) is not equal to the arc that it creates on the circle, meaning I run out of room on the circle by the time I get to my last piece. Is there a way to determine the size of the circle I would need based on the pieces I have? I was thought we could consider the internal geometry a “semi-regular” polygon to determine the necessary interior angles but I haven’t found anything helpful on that front.

Rhino file with pipe sequence and issues attached.

Thank you!
PVC column.3dm (3.1 MB)