3D printed three-sided die


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This is nice because there’s no three-sided Platonic solid, but this way you can have a die with an equal likelihood of each of three outcomes. The same technique could be used to made an N-sided die for any N.

There is a chance (albeit a small one) that the die could land on one of the two ends. So it’s really a five-sided die. But you could just make a rule that that’s a “push” and the die should be rolled again. Of course the same kind of rule permits three possible results from a regular old cubic die, though a person who points that out to the inventor of this clever shape would have to be a poor sport. (Or a mathematician.)


Cool, and very pretty.

Math question: between a coin and a length of pipe, what is the aspect ratio of a cylinder with equal probability of landing on one end, the other end, or the side?

Show you work and any assumptions you make. :slight_smile:

Or you could just use a normal die and count 1 OR 2, 3 OR 4 and 5 OR 6 as your three outcomes.


The link, for those interested in picking one up: http://www.shapeways.com/model/2046022/modern-art-d3-3-sided-die.html?modelId=2046022&materialId=7

Sure, you could, Sergeant Killjoy…

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No, the correct way is to take the result mod 3, heathen.

That’s not a math question, that’s a physics or an engineering question. In math we don’t make assumptions.


The Cow has always been Spherical


Precisely. I guess it’s the programmer in me, but I couldn’t even imagine doing anything other than (1 || 4), (2 || 5), (3 || 6).

I was shocked, shocked to see a different suggestion.


I was always a terrible software engineer.

Assume perfectly elastic and rigid materials for the die and for a flat, infinite rolling surface, because otherwise the answer will depend on these factors. By conservation of energy the die will never stop tumbling. Each side will come up equiprobably, with a value p = 0, for any aspect ratio.

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You can just use a triangular cylinder as a d3, especially if you round off the ends so it can’t balance on them. (Or if it does manage to balance on-end, you call it a critical hit or something.)

This design does look a lot cooler, though.

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I just wish some brave entrepreneur would invest in the 1-sided die:


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Very innovative; very exciting. I wonder could they make a seven sided dice this way? So far the closest I ve seen is the 14 sided dice (which you could just number 1 to 7 twice). Rolling 2 4 siders and subtracting 1 just isn t satisfying somehow. actually, looking at it now, I see it s kind of a variation on a cylinder type die; though very cool looking and a more probably more satisfying to roll.

…didn’t know you could make such a thing!

Nothing difficult about the object at all. Here’s a quickie 5-sided roller that took about 5 minutes to 3D model. Another 5 minutes and the ends could’ve been modeled similar to the pictured version or just do dome/conic end-caps.

T-Splines modeling recipe: Start with 10-segment torus, select 5 alternating faces along the top. Extrude to create spars. Mirror entire object along x-plane. Bridge connect individual ends of the spars. Deploy Rhino’s Twist command.



could they make a seven sided dice this way?

Googling 7-sided dice shows mostly a pentagon extruded in a cylinder style. I are no mathematician, but the different shapes of the faces themselves would alter the outcome, no? Here’s a quickie variation of the die…

and now uploaded to Thingiverse for all…



wow that s great! I love it!

A couple of snips and half-twists and they could have had a 3-sided die that has only one actual side (ignoring the edges).

Interesting and awesome. It doesn’t seem practical for most board games, though. You could probably use it with “Sorry!” or “Life” without changing the game too much.