OctoCube has gone into mass production and is now available as the Octo-Star Cube at the HK Now Store.
OctoCube is a jumbling puzzle, and is essentially a shape-modification of a vertex turning "fracture sliced" triakis octahedron. It turns on six axes, one at each face of the puzzle. Each axis can be turned in 45 degree increments, but only when that face center shows eight-way symmetry. Otherwise axes are limited to 90 degree moves.
The OctoCube 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. OctoCube also requires six M3 x 6mm (up to 12mm will work) screws to assemble, which you'll need to purchase separately. You should not use springs, as they will allow the puzzle to pop apart too easily.
Please note that this model contains two extra small parts. These are backup as small parts can sometimes become lost in the manufacturing processes.