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I was learning how they make stone spheres recently, and they have a great machine for working with spheres which are irregular by 10-20 percent, it's 3 rotating abrasive cups.(yt videos)

However they first angle grind an octogon of stone by hand, and then they wear down the corners using a sanding belt, until they can get it in the automatic sphere grinding machine.

Is there a simple design for a machine into which you could put in a cubic/irregular stone and out would come a big spherical stone?

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If you have a lathe, then you can use a sphere jig.

A video of Adam Savage using one to build a kendama can be found here:

https://www.youtube.com/watch?v=i8GD33DsRw8