Incomprehensible Cube was inspired by an idea from Bram Cohen. It looks like a regular Rubik's Cube, but it has two edges with two peek holes each. Those are the "special edges". The special-edges layer and the two layers behind it can all turn independently. Like a regular Rubik's Cube. The slice layer between the special edges turns like a slice layer, while the two special edges remain coupled to each other. The top and bottom faces are connected with a rod, which can be observed through the peek holes.
The operation of the puzzle as a whole is quite incomprehensible, hence the puzzle's name. The peek holes help understand the operation and orientation of the mechanism. The mechanism is deeper-than-origin cut.
Please order a 3D-printed do-it-yourself puzzle kit from Shapeways at this page (check with Oskar about screws and stickers), or contact Oskar directly if you are interested in obtaining a fully colored, stickered and assembled sample of this puzzle.