@PEC, great info!
The math is way beyond me and your hex sketch animation says it all. So, the size of the hex determines the size of the ball. After creation, one can scale it larger or smaller as needed.
I got lucky with my first video where I projected lines on the sphere. I used plus and minus 20° to create opposite sides of my hexagon. If I used plus and minus 20.905° I should be able make it work. I’ll give it a try. Thanks again for your in-depth summary. Kudos to you!