print design - How do I map Illustrator artwork on a sphere?

I am looking for help with creating spherical map similar to provided in picture: the 6 parts spherical map image setup (bent):

I want to put together a promotional balloon vinyl,and I want to print on advertising material and thus put together a balloon, when put together to be whole advertisement.

My problem is, write logo like this in the figure that, when cut dlove and merge into the sphere of painting merge and be whole