Sphere Surface Dissection, Baseball, Tennis Ball, Math

Printing Advice: Please use support and raft.

Looking at a baseball or a tennis ball, one wonders how to cut a spherical surface into two equal pieces. There are certainly many ways to do it, taking advantage of the spherical symmetries. Scott Elliot has some nice OpenScad code that performs such a dissection. I am looking at the project from a K-12 educational perspective. How can one dissect a spherical surface in Fusion 360 or similar 3D CAD environment?

Well, it turns out to be an appealing effort on Fusion 360, after a bit of mathematical tweaking. We can start with a hollow sphere (the result of subtracting two concentric spheres) and a cube of equal dimensions. After centering the hollow sphere and the cube, we can sketch a circle on a cube surface, whose diameter needs to be such that, if we were to make another circle of the same diameter on another orthogonal cube surface, the two circles are tangent to each other in space. A bit of algebra with the help o