Create a 120-sided disdyakis triacontahedral die as the sphere-like die with the largest number of faces. Anything larger is either cylindricalish or not elegant. 120 has many divisors, so it can be used to generate smaller random numbers.
In practice, it will probably too easily roll off the surface and is too difficult to manufacture without bias.
It is curious that 120 is a little less than perfect powers 11^2=121, 5^3=125 and 2^7=128, or even more curiously expressable as a difference of perfect powers of the same base: 120 = 11^2-11^0 = 5^3-5^1 = 2^7-2^3
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