# 120 Sided Die -- Just Roll With It

A one-of-a-kind die that challenged mathematicians to figure out how to squeeze all those sides and numbers onto one die.
Karin Heineman, ISTV Executive Producer

(Inside Science) -- What rolls, has 120 sides and has no real practical use? It’s a 120 sided die – it has the most sides of any die in the world. There are lots of unique dice sets around – think dungeons and dragons. And there are even 60 sided dice. But this is a one-of-a-kind die that challenged even the best mathematicians to figure out how to squeeze all those sides and numbers onto one die.

Robert Fathauer, PhD, a mathematician at The Dice Lab, and part of the team that invented the die, “It’s an expensive die, but compared to a lot of other things, it’s not a lot of money.”

According to Fathauer, “I thought, is anyone going to pay \$12 for a die there’s no use for? It turns out the answer is yes, but I think it’s just because it is an interesting object.”

It’s not just interesting, it’s mind boggling that someone could design a die with 120 sides. But Robert and Henry Segerman, PhD, mathematician and cofounder of The Dice Lab, have accomplished the seemingly impossible, but not without its challenges.

“Making a large die is more difficult than making dice with less number of faces for a few reasons. For one thing if you have a lot of faces, the faces are small, and so there is less area to land on and sit flat. Also there is less area to put a number in,” said Fathauer.

At 120 sides, it’s also a great number for math related combinations. It’s five factorial, which means: one times two times three times four times five equals 120.

So, if you have five objects, there are five factorial -- or 120 different ways to arrange them.

Making a die as fair as possible means mapping out the numbers equally over the die. To take on the task, another mathematician, Bob Bosch, PhD of Oberlin College in Ohio, was enlisted to find a perfect numbering system for their D-120.

“You’ll notice the numbers are arranged in rings, there’s 10 numbers per ring and there are 12 rings, gives you 120 numbers. It turns out there’s almost 10 to the 98th possibilities for arranging the numbers, and that’s something like a billion, billion times the number of atoms in the known universe,” remarked Fathauer.

For the geometry fanatics out there, do you know the proper Greek name for a 120 sided die -- also known as the D-120?

“Our D-120 is a disdyakis triacontahedron,” exclaimed Fathauer.

It’s a quirky die to say the least, it actually wobbles when it’s rolled.

According to Fathauer, “It’s got some type of pointy features that tend to cause it to lose momentum faster.”

It’s not the easiest die to read, but with a little practice it gets easier says Fathauer, “It’s a little harder with 120 sides to know which number that is. You can actually rotate it a little bit and see that the one face that is straight up will stay in place, it will just turn about the center.”

But despite its oddness and uselessness, it’s neat to toss and twirl around, it has 120 possibilities at your fingertips, and it’s a math lover’s dream.

“There’s no real use for a D-120 at this point in time, you can make something obscure. One thing you can do with any number of sided dice is play math games,” said Fathauer.

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#### Karin Heineman

Karin Heineman is the executive producer of Inside Science TV.