I’m on a journey to turn a true sphere. Plenty of guidance on u tube, but not so smooth in person. This is 2 inches diameter. Started as 2 1/4. Crabapple.
Good fun! It looks like you're well on the way to a perfect sphere!
Mark StLeger showed a nice trick to help refine the sphere. He cut a short piece of what looked like PVC pipe straight across at exactly 90 deg and smoothed the end. Seems like the pipe was maybe 1/2 the diameter of the sphere.
When at the stage of holding it on different axes with cup centers to refine the curves, as it looks like you are in the photo, he holds the end of the plastic pipe against the wood and moves it around on the surface to see where it needs work. When the pipe fits perfectly all over, it's done!
He turned these in a demo at a symposium, turned a round track in a piece of Corian so three spheres fit perfectly. When the top one is spun, all four go round and round! I'm honored to have this one in my display cabinet:
Many years ago I devised kind of a variation of the pipe check method, not to check, but to turn some spheres. I used a piece of steel pipe a little smaller than my intended sphere. Spun the blank on the lathe while swinging the pipe back and forth on the tool rest, sort of like a circular scraper. It quickly transformed the cylindrical blank into one with a marble-sized sphere on the end. It was so easy it almost felt like cheating!
When turning larger spheres I start with the octagon method like you probably did, then successively trim off the "corners", approximate the curve with a spindle gouge, then hold between the cup centers to refine.
JKJ