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Look at the humble d10 for inspiration. The trick is to avoid making a spherical-looking die. A fair d65536 could look like a pair of cones glued together, with 32768 sides per cone. Alternatively, one can make a fair 65536-sided cylinder with rounded ends.



In practice though I'd go with four of those: https://commons.wikimedia.org/wiki/File:D16_HEX_dice.JPG (assuming that I can get them in four different colors)


Blasphemy. Single fair die or bust.




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