I'm trying to make the female part of a ball joint such as:

Except I'm trying to make 3 "dips" instead of the usual one or two. This would leave 3 "fingers" to hold the male ball. The part will be 3D printed and the male ball will simply snap in and hold a friction fit. I can work my way around lofts and simple shapes in solidworks, but this has me beat. How do I make a hollow sphere with a wavy cut around it's equator? I've tried a revolved cut with different guides, as well as a swept cut with different guide combinations but I can't get anything to work. The below example always returns self-intersecting geometries as I don't know how to make the rectangle to stay vertical durring the sweep.

I assume this is an easy fix, and I would appreciate your help. You can attempt to finish the operation from the file I provided but I assume there is an easier/more elegant way to do this all together?