The mass-produced 2x2 mirror cube (2x2x2) is a fine twisty puzzle: it turns extremely smoothly. The face cuts are at 18.5mm-38.5mm, 23-34, and 25-32. Scaling so that the side length is unity: 0.32-0.68, 0.40-0.60, 0.44-0.56. Unfortunately, the chosen cuts result in some of the dimensions being very similar (e.g., 23 and 25mm), so difficult to distinguish from other dimensions, both visually and by touch.
To maximize the absolute difference of dimensions, the cuts should have been chosen as multiples of 1/7, i.e., 0.14-0.86, 0.29-0.71, 0.43-0.57. If one wanted the avoid the smallest cut from being so small, the optimal cuts would still be in arithmetic sequence: 0.32-0.68, 0.392-0.608, 0.464-0.536 (so only the last cut should have been different).
To maximize the relative difference (division instead of subtraction) of all possible pairs of dimensions, the optimal cuts are 0.18-0.82, 0.33-0.67, 0.45-0.55. Close dimensions differ by factors of 1.82, 1.37, and 1.22.
For both of these optimizations, we needed to apply the additional constraint of maximizing the difference, or ratio, between the size of the whole cube and the largest cut to prevent one cut from tending to 0.
Optimization code will be posted later.
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