Check this simple non-digital manual method to flatten the sphere into eliptical wedges, called gores -
http://octopus.gma.org/surfing/imaging/globe.html
With foam having certain thickness I would first do enough number of kerfs to allow for radial bending, then cut these foam shapes with a jig saw or steak knife from the other foam side with no kerfs for
internal circumference surface of the corner.
Then I would tack the shapes together (with
kerfs to outside) with something like tooth picks, or nylon strong ties, or short strips of plywood with drywall screws from inside, or other means and then fill the gaps outside with great stuff foam. I would also not bother doing the shapes to a sharp tip, but rather cut the shapes shorter so that will form a hole in the top of the corner that can easily be filled with Great Stuff foam after the shape is installed in place.
I think that would work..
In this case I would also try using the packing scotch tape on the
inside to fit the pieces together..

Should end up with a good internal surface that way, while external surface can be faired once the GS foam is set.
in boat building they are using thickened epoxy instead of GS foam to fill gaps between foam strips, but that is more expensive and heavier and also not that easy to sand to shape later.