Scaling down Inscribed Squares

Hey,

I had a problem in grasshopper that I was hoping someone could help me resolve.

I have a square or cube that I would want to rotate and scale down using its center as seen in the image. I managed to make the definition so it could scale down using its center and parametrically controlling the number of steps/rotations however the scaling down so far can not be relative to the bigger square

I think it would be pretty clear if you look at the attached image with the current progress and the aim I have. If anyone has any suggestions or improvement in the definition they would be highly welcome and appreciated.

Please find the attached grasshopper file and rhino file for the definition.

Thanks!