## Introduction: 3D Printed Spinning Percentile Dice

I've been designing and printing various odd parts on 3D printers ever since I convinced my wife to let us buy a 3D printer in 2012 after seeing them demoed at Maker Faire. My son grew up seeing printers in action and all the things you can make them. So I shouldn't be surprised when he casually suggested I could make a two part spinning dice based on a dreidel.

Below is the story of how this crazy contraption came to be.

## Step 1: Taking a Design Further, Way Further...

A while back I designed a spinning die with five possible rolls (0-4) for an ancient board game (the Royal Game of Ur) I was making. It was inspired by a dreidel and designed to be easily 3D printed. I showed my son the die since he is really into D&D and thought he would appreciate it, which of course he did!

With both of us being makers as well as engineers (well, he’s still in school studying engineering…) we couldn’t leave it well enough alone and began to contemplate how to take the design further. Of course, he wanted me to make a complete set of D&D spinning dice which at this point didn’t seem that difficult and he agreed. Though, after making one (a D10) we decided they wouldn't be practical since they would spin so long you'd get impatient waiting for them to stop. The idea was too cool though, so we continued to brainstorm.

After discussing various types of dice we could make this way, my son threw down the challenge gauntlet and suggested a 2-part percentile version. A what? My son explained that percentile dice in D&D and other dice games are used for certain actions described in percentages such as if your character has an ability that has say, a 65% chance of succeeding, you need to roll a 65 or lower to be successful (a very simplified explanation). Usually this is done rolling two D10 dice. One for the 10s and one for the digits. “Wouldn’t it be cool if you could use one dice instead of two for this?!” he says… I, not really understanding what he was talking about said, “Oh yeah, of course!”. But how would you do this? Apparently there is such a thing as a dice within a dice, I was informed. The inner dice freely moves inside a larger hollow faceted dice. That’s it! I already made a spinning faceted top like dice, just add another spinning faceted top like dice inside it.

## Step 2: How It Was Designed

So, the problem seemed straightforward to solve - dice within a dice, easy peasy. I began laying out the 10 sided spinning die in Fusion360 the same way I created the other spinning die. Start with a 10-sided polygon, extrude it vertically. I gave the polygon a 1 inch radius and extruded it the same amount. Next, chamfer the top edges all at once with a 45 deg chamfer. There’s your basic shape, a flat faced diamond. On the 5-side die I added a post in the middle and numbers on the flat side lining up with the facets. When the spinning dice slowed down it would come to a stop on a faceted side. For the percentile die, I needed to hollow out the main die and insert another smaller die inside it. To do this, I used the shell command on the main shape. I left about a .375” thickness to allow enough space on the flat to number the larger die. I added a stem to the main die ending flush with the face. The inner die has a hole a bit larger than the stem so it can spin freely about it. The hole has the added benefit of shortening the inner die so it has plenty of vertical space to spin about. It is faceted too, so it will bounce and land on an inner facet of the main die.

I didn’t want to have a convoluted support system to remove when I printed this, so I had to make it a multi-part print and assemble the final die. To do this I added an over-fitting top stem that slipped over the stem on the main die and glued in place. The inner die spins about the base stem and the top stem keeps it from falling out.

## Step 3: This Is Where It Got Real or "Don't Pull That Thread!"

**Editors Note: If you don't care about the physics and mathematics of randomness in dice please proceed to the next step for the 3D files and have fun printing and playing with this cool dice.

After I made the D10 spinning die we were playing with it and reveling in out success when we realized we were getting an unusual amount of the same number. Something wasn't adding up so I decided to do a “little study”. I’d spin the double die fifty times marking down the results of each roll to see if our fears were true. Unfortunately they were. A very large percentage of the rolls landed on either 30 or 40 on the main die. What was happening? I designed the die in CAD, it was perfectly symmetrical. I then checked the 10-sided spin die I made. It too seemed off, favoring the 1 or 10.

Ok, seeing a pattern here. Both dice favored two numbers right next to each other. Obviously they were weighted on the opposite side, but how. Both dice were printed on their side. I had designed them with 45 deg sides so they would all print easily in one piece and you'd get nice legible numbers. Each had 3 perimeter wall thickness and both had 10% hex infill. That’s it! The infill printed vertically, but the dice were positioned at a 45 deg angle. When you stand the dice up straight, the infill is now at an angle. The infill was throwing the weight off!

I modified the dice and printed them flat on their faces resulting in the model printing perfectly vertical. The double percentile die, with it’s 100 possible rolls, was taking too many spins to get a pattern of the randomness, so I focused on the plain 10-sided spinning die. It still has 10 possible rolls, but figured fifty spins should show the range of randomness possible. Well, not so much. The flat printed version still seemed to favor one side. I upped the spins to 100 and the pattern was more obvious. It definitely favored one side. (See the radar charts above which conveniently show how the the dice seem "weighted" to favor certain sides.)

I tried many different options from varying the infill amount to printing with numbers and without. There didn’t seem to be the level of randomness needed for the spin dice to be considered fair. So I tried a standard D10 polyhedral die from my son's D&D set. After 100 throws even it didn’t seem perfectly random - closer, but not perfect. Now I was really at a loss.

I took a step back and did some research on fair dice. If you want to jump down a very large rabbit hole start with a great video on YouTube by Numberphile called "Fair Dice (Part 1) - Numberphile". In it they give a good definition of “fair” and go into a lot of interesting aspects of dice including platonic solids, symmetry and the physics of rolling dice. Pretty heady stuff, but it got me thinking. How would a D6 cubic platonic solid die perform in my impromptu study. After 100 throws I was amazed at it’s near randomness. Maybe there is something to this platonic solid thing.

I was nowhere near an answer except that in figuring out the fairness of my dice you can only go so far. True randomness doesn’t occur except at infinity, and even then, it’s random. By making my spinning die as symmetrical and accurate as possible in its construction and limiting it’s roll (or spin in this case) to one plane (vertical as it spins), the die has as much of a chance of landing on one face as it does another and therefore is more or less fair.

## Step 4: In Summary...

To print your own spinning percentile die, download the attached files. Be sure and print with the face of die flat on the build plate. You will need to glue the top stem into place - a bit of superglue or epoxy should work. Depending on how your 3D printer's first layer is calibrated you may need to trim any flare in the hole for the stem and the top stem as well for it to fit. To assemble the percentile die, slip the smaller inner die over the stem on the main die, then glue the top stem into place . I've included versions with numbers and without in case you want to paint your own numbers on the dice.

For printer settings, I used 3 perimeters for wall thickness and 10% infill. Also, I scaled the original file down by 30% when I printed it. That seemed like a more reasonable size to play with....scale at your own preference.

So, put as much into this as you like. I think this dice design is unique and fun. It will never meet the standards of Vegas, but should provide an interesting addition to your next dice game adventure.

Participated in the
3D Printed Contest