When you click a face, the opposite face doesn't move. The second layer next to the opposite face turns by 90 degrees; the third by 180 degrees; the fourth by 270 degrees and so on.
Acknowledgment:The physical version of 4x4x4 was created by Timur at twistypuzzles.com and published here.
The puzzle uses html5 canvas, which is not supported directly by IE 8 or lower. I also apologize if the animation is jumpy on some browsers. Try using the latest version of Chrome for the best experience.
Nan Ma, 12/31/2012