Fantastic mood, audio, and visuals; game feels good to play and the mechanics are interesting and provide a lot of good puzzle space; progression of levels feels very well tuned, and the puzzles were challenging without ever being frustrating or overwhelming. Incredible job! Only criticisms are with way to tweak and improve the experience: I'd suggest an undo button, and potentially a way to control the camera, or show the unseen sides of the die--I know part of the challenge is keeping special awareness of all sides of the die, but from what I've heard from my own game as well as on a lot of these other 'dice-rollers' people have submitted is that the puzzles can be made tricky enough without that aspect and everyone just ends up wanting to be able to 'see' all sides of the die.
You should be very proud of what you've made!