What's the first fair dice you can't make either directly or by relabeling other dice?
Ex.
d1 = Always 1
d2 = d2 (a coin)
d3 = take a d6 and label 2 sides each 1,2,3
d4 = d4
d5 = take a d10 and label 2 sides each 1,2,3,4,5
d6 = d6
Etc.
We aren't limited to the platonic solid dice, after all a d10 is not a platonic solid.
@urusan its going to be a prime number of sides, wince you can easily get an n-sided die given a- and b-sided dice where a*b=n
using standard dice of the sort you can get at a hobbyist store, you cant get a fair d7
however, d7 do exist: https://commons.wikimedia.org/wiki/Dice_by_number_of_sides#D7
actually, scrolling through that, i begin to suspect that if you want a certain size die you can get it; itll just take something like pic related
@urusan cleverer arrangements are possible, usually also involving leaving some parts of the die round instead of being a side
practically speaking, the die will become more and more cylindrical/spherical as you add more sides, so i suspect the real answer is a surface area:sides ratio, beyond which it just rolls and/or you cant read the numbers