Neat concept, thanks for sharing. Something is not quite right with the rotation matrix or roll transformation code. The die, for example, doesn't always roll deterministically 90/-90 degrees on click. Sometimes it appears to roll 270/-270 degrees to achieve the same state. That visual quirk really impacts my mental model of the die while playing and undermines the entire concept (in my opinion). I honestly didn't have confidence the game would continue working properly and stopped playing.
(Edit: I skipped the tutorial and see it gets complicated with the ability to climb around on the walls. Happy bug hunting!)