Hi, LEN polygon here! In this post I want to share with you the story behind the dUltimate dice.

I'm a product designer with heavy interests in games, math, and programming. As one might expect of a product designer I tend to image new concepts in my daily life even outside of my day job.

At one point I garnered a special interest for dice, specifically their polyhedral shapes. So I started thinking and researching...

### What type of dice are there and why?

Standard d4, d6, d8, d12, and d20 are represented by the five platonic solids. Those are the only convex polyhedral of which each surface, edge, and vertex is exactly the same. I found that these were used as educational dice and somewhere in the 20th century got picked up by tabletop RPG's and wargaming as dice with different purposes.

The d10 came along later due to the need to often roll a number 1-10 or even roll 2x d10 to create a percentile (0-99). Due to there being no platonic solids left and none of them having 10 sides at some point someone made a 10 sides dice using two 5-sided pyramids stuck together creating the known Pentagonal trapezohedron.

So now a standard 7-piece dice set for D&D (dungeons and dragons) and many other TRPG (tactical Role playing games) consist of a d4, d6, d8, 2x d10, d12, and d20. Often called polyhedral dice set, DnD dice set, or just "math rocks".

Many like this setup and are creating all kinds of fancy design with inclusions, metals, gemstones, or other fancy materials!

### What's the largest die?

... but I got more interested in the polyhedrons. How large can we go?

Well, someone figured that out already. The Dice Lab created a 120-sided dice (d120) based on a Disdyakis Triacontahedron. They specifically figured out that this is the largest you can go in constructing a fair and useful die. The only way to go larger would be to take the same d10 approach and stick two n-sided pyramids together, or take a cilinder with n-sides. But that quickly becomes unpractical to fabricate... I mean using two 60-sided pyramids together to create a new type of d120 would result in angles of only 6 degrees between faces. No manufacturer will be able to create that within tolerances for a small die!

### What about multifunctional dice?

So what else is there to explore? Has anyone ever thought about combining all those different dice in a single dice somehow?

Once again the answer is YES. Game Science actually released the D-total design which is a 24-sided dice which has a clever layout allowing it to be used as 18 different type of dice. Woah, 18! I got curious and wanted to understand this design more, but the more I read about it the more I saw flaws in the design which made it unsuitable for a lot of gamers in my opinion:

It has too much going on on each surface making it very time-consuming too read. This D-total can do too many different things;

Many of the 'type of dice' on the D-total have a known marking, but other ones are unfamiliar to many;

When rolling some type of dice it can be required to reroll your die. For instance if you want to roll a d20 with the D-total you look at the central number which goes up to 24. So if you roll above 20 the manual says you need to reroll. Same for the d10. This is understandable in the design because 10 and 20 do not fit perfectly in 24, but this is unacceptable for many uses because of the popularity of d20 and d10 rolls in TRPG's!

### The first idea for the dUltimate

Here, I could see my design come to live. I wanted to design a multifunctional dice that can replace a full 7-piece dice set (d4, d6, d8, d10, d12, and d20) without requiring rerolls and all while optimizing readability.

I started looking at ways to combine these numbers individually: 20 is divisible by 10 and 4, 12 is divisible by 6 and 4, and 8 is divisible by 4. So we can spot these 3 groups of two (20&10, 12&6, 8&4), but nothing more. Are there any larger numbers that can be divided by all of these mentioned numbers?

Well what do you know? It's 120.

And I learned not too long ago that this is the largest fair dice possible. So at this point I know what I have to do: design a 120-sided dice that cleverly fits all the other dice on it without becoming an unreadable mess or a dice the size of a football...

### Next up: dUltimate dice design iterations

In the next post I will write some more about the thought behind the design and the iterations. Feel free to let me know if you have any questions or comments.

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