Dice sums

How many ways can the numbers on n dice add up to m?

For example, with two dice, there are three ways to get a total of 4: 1+3, 2+2, and 3+1.

The algorithm run by this page, and the maths behind it are based on an article by Alasdair McAndrew, which can be found here.

I'm very grateful to be able to use the JavaScript BigInteger library version 0.9 by Matthew Crumley, see this page.

Number of tetrahedral dice:
Number of cubic dice:
Number of octahedral dice:
Number of dodecahedral dice:
Number of icosahedral dice:
Sum of numbers on all these dice:

Multiple Platonic dice sums