How do I 3D-print fair dice?

Question

As 3D printers become more and more reliable, their prints get better and better. But FDM printers do have their problems too: you print tiny ovals that smooch together at the edges, and infill makes it awkward at times. So, how do I make a 3D-printed die fair (as in: not favoring one side too much)?

Answer 1

This is going to become a 3-step answer, as 3D Printing uses 3 different steps: Design, Slicing & Material choice before I elaborate alternate ways to some fair dice. Yet, we start with the material, as we need to know about it first. In this case it does impact everything from design to slicing and the print.

Variant A: Printed perfect(?)

Step 1: Know your material

Let's face it: most materials used in Fused Deposition Modeling (FDM) face an non-homogenous shrinking between XY plane and Z axis. But if you know these specific properties for your printer/filament/temperature combo, you can compensate for that. Know your material - you will need that for slicing. Run a test print of a 10x10x10 mm cube and measure - the offset of the 10mm on each axis is what you need to compensate for via your slicer.

Step 2: Design fairly

Platonic bodies

When designing your STL, try to design as fair as you can. Either indent the numbers as little as you can while maintaining readability, or, if you have a 2 color printer, fill the numbers with same density material but from the other color.

Another thing to consider: indent the same surface area on each face of the body. That way you remove the same volume and thus same weight from each face, making it somewhat fair in the design, as the Center of Mass should be mostly in the center of the body now.

Prism-"dice"

A cylindrical (or rather: prism) design that is rolled over its "cylinder" surfaces might be the most easy to be designed fairly and be reasonably easy to slice, without having to resort to specialist slicing methods and tons of different compensations to keep in mind or having to assemble the object after print. It might be made with or without a "fall over" cone/elipsoid shape at both ends. Or it might be made like a dreidl, having only one conical/elipsoid tip for easy printing, possibly even havign the 'stem' printed as a different object and then assembled after print.

Step 3: Slicing

Now, there is a pretty fair design... but what settings to use when printing it?!

Infill will make it wonky, so there are 2 options: solid (100% infill) and fully hollow (0% infill). Solid is easier to print and heavier. Hollow saves (depending on surface sides) 95% or more of the material in contrast to solid but can fall victim to sagging flat surfaces or wall thickness being not the same as flat area thickness.

Now, after we chose the infill settings, we need to choose some other things. We want to print fairly delicate stuff, so we should use a smaller layer height than normally (0.05 mm, for example), and better a smaller nozzle - 0.2 mm or even less, if available. This again means, calibrating the printer/material combo for these two settings (XY / Z shrinking).

After calibration, finally print! The dice should be pretty ok in fairness with that, but they are still not totally fair...

Extra-step: Postprocessing

You might make a test for bias by floating it on a salt water layer under tap water... if you managed to get it solid enough to reduce the air inside it to make it sink between these layers. That way you can slightly sand the heavier side until it is unbiased.

If you manage to print somewhat fair and hollow, you might consider filling the cavity with some kind of resin (for example epoxy) to give the objects a bit of weight. This has some caveats on its own though: you'll have to leave a filling hole and you'll have to coat the inside equally or refill it several times to ensure a complete fill as most resins shrink when curing. Also, most resins heat up in curing, though usually not to the degree it melts FDM. As you work with resin, Wear gloves as it is aggressive to skin!

BUT! 3D printink can do more!

Variant B: Printed Perfection

FDM is home printer stuff, but maybe you have access to something more... industrial. They are tricky in their own way, and you better know what you do with them.

SLS (solid laser sintering) You just need to know your material shrinking coefficients in that case... and no, you don't need to think about infill, you only can do solid, 100% filled objects this way. But you will also have virtually no air in your print. Having SLS at home is rare though. This is however likely what you get when you order printed... but remember: the SLS powder is highly hygroscopic and will need to be sealed. Also, it does turn yellowish over time if it starts white. Using reused powder to a large degree degrades print quality also. And never look into the working machine.

DLMS (Direct Laser Metal Smelting) is quite new and pretty much the metal variant of SLS. If you make your dice in that way and get them almost indistinguishable from cast metal. Polish the surfaces a little, don't sniff the breath the powder and don't look into the laser.

DLP/SLA (Direct Light Processing/Stereo Lithography) Printing the thing from curing resin actually is pretty much close to SLS, but it has some resemblence to FDM in parts... biggest benefit: you can make very delicate details, and your layer heights get really thin - and you have a huge array of colors to choose from. But you have to take in mind, that you might want to either make the dice solid or design them with a hole in each of the sides or corners to allow surplus resin to flow out. You get perfect surfaces and can reuse the resin for quite a bit^{depending on printer and storeage}, but remember: SLA is a stinky thing, never look into the printing machine & the resins are very agressive to skin, so use gloves when working with the printing and the print until properly cleaned.

Variant C: Lost Print

But wait, what if you don't actually print the dice but just print a positive of the dice and then make a negative mold from that?

Yes, that can be done. You know lost wax casting? There you go. Here's your step by step:

• Print your dice.
  • maybe even puzzle the positive together from several faces printed all in the same orientation for maximum equality in the print.
• Add a casting inlet and air outlet to the print.
• cast the positive in either a clay material or gypsum. Allow it to dry/set.
• Burn/melt out the positive, you get a hot and empty negative form.
• cast in liquid metal or a resin
• break mold, remove the inlets, polish some and... voila!

If you are good at green sand casting, you might use that instead of lost wax casting - and reuse the positive for a second casting. Or, if you are good, you can make two-part molds that are reuseable.

Variant 3b: mold it!

If we can print a positive and make a mold from that, we might as well print a mold directly. We can just cast in "cold" materials then, but if you have something that can be cast that way (some resins or wax) you can make either the dice or casting sprues for lost wax casting that way. Designing here will be different on the last steps though: after doing your wanted object, use this as a "tool" to cut out from a more or less square block that surrounds it. cut out the inlet/outlet for material and air from the block. Then cut up to your liking, if you want a reusable multi-part mold. You might want to add a roove to add wire or a rubber band around the print to keep the mold together while casting.

Or we go industrial with that model, grab a CNC and make the mold halves that way and give up on printing the dice...

tl;dr:

Know your printer, know your material, design for your printer's requirements, design fairly, maybe avoid printing the actual dice but print a positive to be molded and cast or print a mold.

Answer 2

Honestly, I wouldn't.

You can find dice templates at places like thingiverse, but with my (admittedly limited) experience of affordable 3D printers, I would be highly skeptical that the machine tolerances are up to snuff for producing a fair die.

See this discussion from the 3d printing exchange, especially these two answers.

If you're really bound and determined to do this (we all have our geeky little passion projects!) I'd advise trying to find a template which the authors claim to have tested with chi-square, then find out what (type of) device they used. If you can replicate that, go for it... and then do the chi-square test yourself. It's ridiculously easy to set something up wrong, or forget something (like the possible effects of internal orientation.)