The Pentamid puzzle is based on the geometry of the pentagonal dipyramid. It turns on the five edges around the equator of the puzzle, as well as on the two polar vertices. Each vertex can turn in increments of 72 degrees, while the edges are limited to 180 degree turns. The Pentamid puzzle becomes scrambled fairly quickly with just a few turns.
The Pentamid puzzle comes as a DIY kit of parts, and you will need to supply your own stickers. The templates for the stickers are available in the instructions forum.
I recommend that unless you are familiar with the process of dyeing these parts, you purchase the puzzle in "Black Strong & Flexible". It costs a bit more than the white material, but it's worth it since the finished puzzle will look and work better. Pentamid also requires screws and springs to assemble. These can be purchased through a few different online puzzle sellers. The springs I used came from this shop. You'll need seven of the springs, combined with seven 12mm M3 screws, which you'll need to purchase separately.