Here’s an awesome 360 degree 3D printable GoPro mount via Reddit. Take this concept 1 step (2 cameras) further, and one can get an amazing spherical panorama video seen after the break. The site is in German, but definitely worth checking out.
As for how to process 6, or even 4, GoPro videos together into something coherent, I have no idea. Apparently it has something to do with computers.
Edit: Per Mark’s comment below, “Kolor Autopano” is apparently the software used to combine these videos.
On the other hand, if you have a 3D printer, the information on printing one of these can be found here. Personally, I might just kludge one together with duct tape or whatever was around, but to each his own…