You’ll need the classic d4, d6, d8, d10, d12 and d20. For those of you who don’t know, these are dice mapped out on regular polyhedrons, except d10, which is mapped out on… something else. You might want some in front of you, or if you’re a criminal mastermind, you could visualize them.

First, take the four sided die. As long as it ‘works’ (eg. has all the equal numbers in the same corner, so that it’s possible to see what you have rolled), it doesn’t matter how the different numbers are related, all you have to do to see a given combination (1 over 2 and 3, 1 over 2 and 4), is turn the die.

Now, if you’re with me, this means that you don’t have to work out a pattern for mapping out the die, as any working die would include all possible relations. (Actually, you could have two different sequences for each of the lower numbers (1 over 2 and 3 differs from 1 over 3 and 2), but no different sequence will be more harmonic than any other (One could say that 2 and 3 is more harmonic than 3 and 2 because they are then in order, but no reading direction is inherently more harmonic)

Then, take the six sided die. As most would know, it is generally agreed that the sum of all pairs of opposing sides should be the same. Let’s adopt this as a rule. Now, lets look at the die with 1 as the side facing up. 6 is facing down, but how do 2, 3, 4 and 5 relate to 1? 5 can’t be next to 2, and 4 can’t be next to 3. Thus 5 is next to 4 and 3, with 2 opposing. It wouldn’t really matter if 4 is left or right to 5, as again, no reading direction would be inherently more harmonic.

So it seems quite simple rules apply to d4 and d6. How would you map out the remainig dice?

A friend and me thought we had beat the dicemakers to it a couple of years ago, but we examined them again tonight, and found even cooler patterns as they are.