Logical cube - 4x4x4
This 4x4x4 logical cube is a more daunting challenge than the 3x3x3 cube. The number of pieces is far greater, and there are no "fixed" pieces to serve as a reference.
The puzzle has an ingenious mechanism. The sphere has eight perpendicular grooves, aligned two by two, for the center tiles to slide in. A specially shaped steel frame prevents the sphere from becoming misaligned with the rest of the cube. There are two edge pieces at each face intersection.
Here are more details about the 4x4x4 logical cube. Also, The Magic Polyhedra Patent Page refers to the patent.
Patent no. RO 106960 B1 / 1993-08-30