For this lens, the horizontal field of view is 142 degrees and the vertical field of view is 94 degrees -- typical numbers for a "180 degree diagonal fisheye" lens. The other style of fisheye is a "circular" fisheye. These get 180 degrees in every direction. The resulting image is a circle rather than a rectangle. If you have two photos in opposite directions, then you've got a complete 360-degree environment map.

The guys who do kite photography do this to get beautiful panoramas. The kite shoots down at the ground, and then the photographer, holding the same camera later, shoots straight up in the sky.

Another way you can do it is to have a mirror ball. Here's a fascinating page with closeup mirror-ball panoramas.