One of the things I enjoyed about the Hellraiser Mythos is that the puzzle cube is an impossible object. For it's clockwork mechanism to actually work the way it's depicted on screen the gearing has to exist in an n-dimensional space. The internal mechanism must have parts that slide in and out of 3-dimensional space to account for all the gymnastics it performs on screen. Sure, you can excuse that behavior with "It's magic!", but that seems to fly in the face of LeMarchand's engineering expertise.
This was an attempt to account for one particular on-screen movement, the rotation of alternating prisms along the vertical axis seen in the first three films. Just right click and open the image in another tab to access the full-size graphic.