The Invention of a New Kind of Dice

HexaCubes were invented by James Kelly. It started out with a very small problem. Kelly had created a role-playing system called the Amplifier System for his (allegedly) amazing role-playing setting, Inner Skies. This system resolved almost all of its rolls with a percentile role and a d4. While very satisfied with the system, James noticed for the first time that typical d4s are pretty lame. They just kind of flop around the table and you always have a sneaking suspicion that you might as well just be placing the die on the table, instead of rolling it. This isn’t really true—but it sure feels that way. James also discovered that other people had already noticed the Lame D4 Phenomenon. No one thinks it is a terrible, terrible problem, but 4-sided dice could be better.

Another problem James had was that he was a incompetent artist. You don’t have to take my word for it. James made most of the graphics on this site. Let’s face it, they are functional, but not that great. So, James decided to combine this problems of lame d4s and a lack of art for his game by making a crowd-sourcing campaign to raise funds for an illustrator for Inner Skies. Easy peasy, right?

Finding a better d4 was very simple. In fact, it would become a mystery to James why we even use tetrahedron d4s in the first place. A major dice company makes 12-sided d4s. Other companies make 8-sided d4s. James bought a few and people universally thought that they were awesome. Lousy d4s were a problem that nobody realized they had.

James noticed that there was a 12-sided shape called a rhombic dodecahedron that had been used for dice before, but not very much. So, Plan A became to offer rhombic dodecahedrons numbered 1–4 three times as swag for his fundraiser. But, James got to thinking. Wouldn’t it be cool if he offered some clever d10s as well? This is where things got out of control.

(Sourced from Wikipedia)

Finding a novel d10 was a much more difficult problem. James’ first thought was to remove two points from a d8 (octohedron). There had to be some proportion that would make a fair d10. This had been done before a few times. There is an obscure oversized exercise die that one can throw to randomly select push-ups, curls, or whatever. Ultimately, this shape of die is not very good. Dice of this shape are not very pleasing to roll or read. Also, they are not very fair because rolling them end-over-end is very different from rolling them with the removed ends parallel to the table.


So, James searched around for a better alternative. Since he hadn’t really thought much about geometry since college, he spent a lot of time trying to solve the problem in a lot of dumb ways. If it were not for this flailing approach to problem solving, James probably would not have ended up on Gerard P. Michon, PhD’s website called Numericana. James was reading an article about what the fairest proportions would be for a shape called a truncated octohedron, which has 14 sides. It is like the exercise die above, but has all of the points removed. Truncated octohedrons have cuboidal symmetry, which is much better than the bipole symmetry of the exercise die. This truncated octohedron shape is used for a traditional Korean drinking game die called Juryeonggu. While reading this article, the inspiration that would lead to HexaCubes hit James.


Would it be useful to make the die more unfair? If the six square sides landed twice as often, it would be like having 20 sides to work with. It soon became clear to James that it might be possible to apply this principle to all of the standard polyhedral set. However, he quickly discovered that he would need more shapes. Because a 12-outcome die cannot be put on a truncated octahedron, James eventually found the chamfered cube shape that he uses for HexaCubes now. Using 3d prints, thousands of dice rolls and the mathematical assistance of his brother, Dr. Ryan Kelly, James was eventually able to find a function that would predict the correct proportions of the dice.

An Early Form of HexaCube Dice

At that point, James had designed a functional set of dice, and was satisfied that this idea had apparently never been used. James decided to take the leap and try and bring these dice to market. He hired an attorney and applied for a US patent. In summary, this is the definition of James’ invention:

This invention is a gaming die that uses a combination of incongruent sides and a number of sides that is greater than the number of outcomes to produce practically fair results.

James would spend a great deal of time refining the invention into its final form. There are several possible configurations of a HexaCube d6, for example. James tested all of them to come up with the most user-friendly and accurate dice he could. A major concern was how the user would be able to easily tell the dice apart. James experimented with several methods, until deciding on the ‘tall-wide, square-diamond’ system.

James would eventually choose the chamfered cube as being the best shape for all of the dice. Chamfered cubes have the most sides without having too many. The more sides a HexaCube has, the more redundancy can be used. Also, it is easier to manipulate which type of side a player rolls when there are fewer sides. This is virtually impossible with a chamfered cube without taking extreme and extremely obvious measures. Eighteen is also the smallest number of sides that work for every kind of die in a polyhedral set, once you figure out how to handle the d20. There are shapes with more sides that might work, but the next candidate has 26 sides. 18-Sided chamfered cubes are much more pleasant to roll.

Throughout the project, James began to realize that HexaCubes are not just different – they are better. In addition to the d4s that roll like actual dice, HexaCubes feature far more accurate d20s that are less likely to roll under your game master’s nasty couch. It has been a long process to find the best final form, but James is very excited to see what people think about HexaCube dice.