The CubeLab 1CM 3x3x3 is a very impressive cube, it weighs just 1.4 grams and is just 1cm in size and yet it still turns decently. It is not really speedcubeable due to its insanely small size but it does at least have some corner cutting (18°) if you force it, I would recommed trying to turn as carefully and accurately as possible.
You can buy it here:
