Thankyou Psygorn.

I'll check out the 7-leafer.

As for the 10*PI circumference at 60 degrees, it is simply because Cos(60degrees) = 1/2.
( Basic triangle characteristics, and/or basic trigonometry. )
ArcLength of latitude circle = ( 2 * PI * circle radius ) = ( 2 * PI * Cos( 6Odegrees) * Sphere Radius ).
Note that formulas vary depending upon use of degrees versus radians.

I relatively quickly used MoI to test every few degrees between 32d and 61d, for convergence of North pole arclength * 6 versus latitude radius. 60 degrees is not practical. I'll stay down around 30d +/-, and abandon fixed hinge pins for greater than 5 leaves.

Shell of leaf looked cool. Had to Flip surface normal.

Best method to create spherecap?
Choices include sphere trim or boolean with plane or line,
There can be some artifact surface(s).
Or revolve of North pole arc to latitude point.

Looking forward to release of your design.

- Brian

The 7 leaf orbox is mighty fancy!