[nmzummrh] Rubik's controller

Create an electronic controller shaped and functioning like a 2x2x2 unstickered Rubik's cube, but with a button added to the center of each face.  (Don't know what to do about the face cuts going through the button.  Maybe the button is divided into 4 buttons.)  It has sensors on it that allow it to function as a controller for a virtual NxNxN cube (or more generally any cuboid N1xN2xN3).  With the buttons, select the depth, i.e., the number of layers to turn.  Twist the controller cube to accomplish the turn.

Orient the entire thing.