Title made me think of Katamari Damacy.
The idea of being able to change levels with the roll of a die is very interesting. Maybe there should be a way of re-rolling after entering a level. It would be very cool if you could see the non-selected levels on the side faces of the dice.
I had some repeated levels, I don't know if that's intentional?
I would like some more visual indication of what's bad to stand on. The dice faces seem perfectly harmless, but they send you back to the checkpoint. And there are some white blocks you can stand on, and others you cannot, which is a bit confusing,
I couldn't figure out what to do with the purple door, so I quit there.