The QuadStar puzzle is based on the geometry of the snub disphenoid. The four five-sided vertices of the snub dishenoid have been elongated to produce true five-way symmetry. These four vertices of the new shape have been made into the rotational axes of the puzzle. QuadStar is a jumbling, but non-shape-shifting puzzle, in a similar manner to my Fracture-10 and Fracture-6 puzzles. Each axis can turn in increments of 72 degrees, but sometimes axes become blocked if edge pieces are flipped in the wrong direction.
The QuadStar 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. QuadStar 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 four of the springs, combined with four 12mm M3 screws, which you'll need to purchase separately.