Ok, so I had to solve a similar problem for my lamp generation software. Basically what I did was to calculate a parabolic arc that would describe the arc of each slice of a ellipsoidal form and then calculate the values of the arc to determine the curve for each slice. I thought I could adapt my lamp code to generate a form that would be useful for you, and I did.. sort of. The problem is, since I'm using a parabola described by 3 points to generate my curves, it doesn't quite generate the correct curves for a sphere. Instead you sort of get a spherical-ish object with slightly pointy poles (below and attached):
Anyways, I know it's not perfect, but I've included a pdf of the path for once side of it if it's at all helpful. If you do use the path I provide, I would recommend testing it at a smaller scale first as my math is probably not 100% perfect and I had to scale it up to create a shape that was 9 feet in diameter. My advice for a perfect sphere would be to use something like rhino or 3ds to generate a sphere and then use the uv unwrap function to generate the parts. You could also try uploading a model into pepakura: http://www.tamasoft.co.jp/pepakura-en/
If you do figure out a geometric solution, please let me know what it is, I'm really curious myself! Also, if you want to know more about the math I'm using for my shapes, let me know.