Some time ago, I built myself a panoramic head that allows for full 360 degrees panoramas in both space angle directions. The point of such a head (I'll post some pictures and instructions later) is to allow you to rotate the camera/lens combination around its entrance pupil and not its nodal point as you will often read, to avoid parallax. Now I used to shoot panoramas using my normal wide angle lens of 18 mm (28 mm equivalent in35 mm cameras) which made it necessary to shoot 32 portrait-oriented pictures for a full panorama, 4 at 60 degrees down every 90 degrees, 12 at 30 degrees down every 30 degrees, 12 at 30 degrees up, and 4 at 60 degrees up. Rather tedious indeed. So I got
myself a fisheye lens (the 10.5 mm Nikkor) which has a much wider field of view. I experimented with some patterns. The most popular on the web seems to be to shoot 4 pictures in landscape horizontally at 90 degree angles and then make a nadir and apex shot. These are very tough to stitch, so I settled on a much smarter strategy that gives way more overlap between shots and is far easier to accomplish since you do not have to change the camera from landscape to portrait orientation, but you can keep it on its side. The pattern is simply 4 pictures at 30 degrees down every 90 degrees and then 4 pictures 30 degrees up every 90 degrees, but shifted 45 degrees from the bottom row.
This can then be easily stitched in a program like hugin to the result below: