Beautiful problem and solution, thanks for the demo and anniversary reminder! We also have have SpherePoints, that probably uses similar optimization methods (just guessing). And probably things like DelaunayMesh should help to find the polygons.

DelaunayMesh for 3D are creating tetrahedrons. So, it is directly maybe not applicable to this. I will have to look into this further if we can find ways of using tetrahedrons and not triangles. But I suspect, that in the process of making it simple in the first section, if I would be making it more complicated in the subsequent sections. If I can make something useful, I will definitely share. Thanks for the idea!

Yes, the definition of 'poly' was missing, corrected now. Thanks to both of you.