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?
Once you get past the usability choice of using pips vs. Arabic numerals (because you can read pips in any orientation), it's more about taste than readability.
Comparing Asian dice to European dice (courtesy of wikipedia) makes this clear:
The color of the 1 and 4 in the Asian patterns is a cultural adaptation (these designs would be considered "unlucky" if they weren't colored red), but the clustering of the dots in the Asian patterns allows for the corners to have more wear (because the pips are further away from the edges), and the pips become larger for the smaller numbers vs. the uniform pip size on Western dice.
Dominoes are adapted from western dice, as opposed to the other way around, which is why they share pip patterns. Mahjongg tiles and playing cards, which don't share this heritage, arrange their pips differently.
If you were to try and make dice extra-readable, I suppose you'd want to modify the Asian patterns (which already have different sizes of pips for each number) but make them all different colors as well, or at least make odd-numbered sides a different color from the even-numbered sides.