This is nice because thereâ€™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 itâ€™s really a five-sided die. But you could just make a rule that thatâ€™s a â€śpushâ€ť 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.

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 Killjoyâ€¦

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

Thatâ€™s not a math question, thatâ€™s a physics or an engineering question. In math we donâ€™t make assumptions.

*The Cow has always been Spherical*

Precisely. I guess itâ€™s the programmer in me, but I couldnâ€™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.

You can just use a triangular cylinder as a d3, especially if you round off the ends so it canâ€™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.

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

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.

â€¦didnâ€™t know you could make such a thing!

Nothing difficult about the object at all. Hereâ€™s a quickie 5-sided roller that took about 5 minutes to 3D model. Another 5 minutes and the ends couldâ€™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 Rhinoâ€™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? Hereâ€™s a quickie variation of the dieâ€¦

and now uploaded to Thingiverse for allâ€¦

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 doesnâ€™t seem practical for most board games, though. You could probably use it with â€śSorry!â€ť or â€śLifeâ€ť without changing the game too much.