Curiously can't made the Boolean Diff (Horizontal + Vertical) in only one Pass ! Is that normal?(
(Just replace the sphere dissected by a new sphere in the file linked)
For Tyglik or Michael : a function explode will be cool !
Made that by hand is an headache as soon as more 10 objects! Select all objects, point a Center, make a "spherical" move = Horizontal + Vertical
or other tricky moves x y z :)

(on the image yellow grid and texts Vertical & Horizontal are inversed but no matter :)