I present my new puzzle - Clockwork Master Pyraminx. It looks just like an ordinary Master Pyraminx, but there's a tricky hidden mechanism inside.
If you turn a corner, the middle layer also turns, but by a smaller angle. Every indivisible turn brings all 3 non-trivial layers to different orientation. That is, one of them stays unturned, the two others are turned by 120 degrees in opposite direction to each other. Repeating the same turn 3 times brings the puzzle back to the original state.
You can not turn the layers as freely as you may want to, but neither the puzzle is bandaged. Do we have a term for this? "Dynamic bandaging"? http://player.youku.com/player.php/sid/XMzE4MDk5ODAw.swf