This is a really unique and really clever mechanic, I love it.
The graphics and audio are perfect for the style of game, feeling extremely crisp and clean but never intrusive. The number of sides matching the current number was a very nice touch.
I've seen from the comments below that you've updated the tutorial from whatever it was originally - if it's any help I can confirm that it works really well now, I was able to get my head around the concept very quickly and get right into gameplay.
I found I was able to get an infinite loop when playing on longest cycle - not sure that there's any real fix for it though given that it's inherent to the mechanic.