I noticed dice and dominos both use the same convention for dot placement. Is there a reason for this? Is there any research on how to layout dots so that they are most readable?
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These dots are known as pips. Pip placement tends to follow a convention, but this placement may vary by region, as you can see by this comparison between Western and Asian dice (from wikipedia):
I suspect this arrangement has nothing to do with cognitive science or usability, but is simply a convention. However, you may note that on the Western-style dice, pips are arranged so as to maximize the distance between any two pips while maintaining symmetry-- this should aid in quick recognition regardless of how the dice are rotated when they land.