# What's the best way to distribute numbers on the faces of a D120?

**doctorow**#1

At first I thought, “That’s a hell of a lot of work to distribute numbers on a die that, if precisely machined and decently rolled, should generate perfectly acceptably random rolls no matter how the numbers are distributed.” But then I remembered: they’re making a D120.

Nerds.

What’s the best way to distribute numbers on the faces of a D120?

*/rolls D20, checks tables*

**nimelennar**#5

It features 120 scalene triangular faces and 62 vertices. That creates the largest number of symmetrical faces possible for an icosahedron and the biggest, most complex fair dice possible. To be considered fair, a dice must be equally likely to land on any of its sides when you roll it.

Do we have any mathematicians in the house who can explain:

- Is this true? Is it impossible to create a fair die with more than 120 faces?
- If so, can you explain why, in layman’s terms?

Thank you!

Each of the 120 sides is 6" wide. Now it’s just a challenge of picking it up for the throw.

**emo_pinata**#10

As someone who is a big fan of BRP based games, this was literally my first thought.

I’ve seen one of the d100 novelties before and those never seemed to stop rolling so I can only imagine what a d120 would do.

**atl**#11

I was trying to teach my kids about the pointlessness of playing the lottery when it was north of a billion dollars and so I pulled out 8d10 – so as to generate a random number between 0 and 99,999,999. And each of them could pick one number. I told my kids they could roll the dice *as many times as they wanted* and if they either of them got it right, I would give them $1,000 each to spend on anything they wanted. The only condition was the game was over once they got bored and wanted to leave.

As you can imagine, the kids thought this was a great idea and rolled, enthusiastically, over and over again. They older kid gave up after about 5 minutes. The younger one stuck it out for about 3 or 4 minutes beyond that, totally dejected at the possibility of winning my game. I imagine if I charged them a nickel a throw it would have lasted about 90 seconds.

Best use ever of my dice collection.

**telecinese**#12

Yeah, I think the next design challenge is finding an actual good use for a 1-120 throw.

**d_r**#14

This is really really far from my specialty (you want a low-dimensional topologist here), but I believe the situation is that you want a die where all the faces are the same polygon and where it is “transitive” in the sense that you can get from any face to any other by rotations or reflections. This puts you in the category of Catalan solids, which are the duals of Archimedean solids (dual means vertices become faces and vice versa). The reason there is a limited number of Archimedean solids is that in any such you can write down some relational conditions between various integers that arise in a natural way in the figure, eg number of faces meeting at a vertex, and then show that there are only finitely many combinations of integers that meet these conditions. I know this is horribly vague, but it is the best I can do without either doing some research or tracking down my recently-retired colleague who really knows this stuff.

**d_r**#17

I’m already slacking by reading BB. I have a stack of ungraded final exams sitting across the table smirking at me.

**henryseg**#18

You can make a fair die with more faces in principle: take two 100-sided pyramids and glue them base to base to make a d200. The problem with doing this in real-life is that it becomes impossible to tell which side is up - we tested a 3D printed d100 designed like this, but the angle between faces is so shallow that it doesn’t show a choice of number well, and the slightest rounding of the die makes it into two cones. The d120 is a little tricky to read, but it is much easier in person - it’s harder to tell from a photo or video.

**Boundegar**#19

Trouble with that is that the probability of a roll with a finite number of digits approaches zero.

**Aloisius**#20

Could you make them out of clear plastic, fill it with colored water and leave a small air bubble or something that floats inside to show you which face was up (kind of like a magic 8-ball)? It would be awkward, but you could read it.

Though I suppose if you’re going to do that, you might as well make a perfect sphere and put as many “sides” on it as you could print.