I did this I made a rectangle split into grid and then applied a Envelope Distort>Make with Warp I reflected it as a copy and arrange the two appropriately.
Then made that a symbol and then made a sphere with settings of 0,0,0 and map the symbol and resized it to fill the front face of the globe.
You may have to modify the warp and the rows to your liking and that will take some wrk and ingenuity on your part but this is a way of a chievig what you want probably other ways as well.
Finishes it ... yey!... It took time for me to figure it out in details but I was able to do it.. Thanks to you a lot...
You could just change the 3D shading to "Wireframe". Then expand it and use Live Paint to fill in the areas.
Are you certain about that Scott take a closer look at the configuration the OP wants to end up with.