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A new pyramid-like shape always lands the same side up

quantamagazine.org

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Re: A new pyramid-like shape always lands the same side up

#121

Post by layer8 »

lloeki wrote: post #114
gerdesj wrote: post #51

Earlier quoted context omitted.

Love it - any sphere will do. A ping pong ball would be great - the DM/GM could throw it at a player for effect without braining them! (billiard)

Nitpick: one of the properties of dice is that they stop on one side (i.e they converge towards stable rest on even ground) and the typical rule is that when they come at rest because of something other than even ground then the throw is invalid. So while a sphere has only one side it basically never comes at a stable enough rest unless stopped by uneven ground (invalid throw), and if it stops because of friction it…

Yes, it’s more like a D0.

It’s debatable though whether a sphere can constitute an edge case. ;)

Re: A new pyramid-like shape always lands the same side up

#123

Post by ColinWright »

The paper says:

"What did appear as a challenge, though, was a physical realization of such an object. The second author built a model (now lost) from lead foil and finely-split bamboo, which appeared to tumble sequentially from one face, through two others, to its final resting position."

I have that model ... Bob Dawson and I built it together while we were at Cambridge. Probably I should contact him.

The paper is here: https://arxiv.org/abs/2506.19244

The content in HTML is here: https://arxiv.org/html/2506.19244v1

Re: A new pyramid-like shape always lands the same side up

#124

Post by riffraff »

stavros wrote: post #119
lloeki wrote: post #113

Earlier quoted context omitted.

There's a link to a D2, where prior to clicking I was thinking "well that's a coin, right?" until I realised a coin is technically a (very biased) D3.

Huh, now I'm curious, what did the D2 look like?

Lenticoidal, I guess? I.e. remove the outer face of the cilinder by making the faces curved

Re: A new pyramid-like shape always lands the same side up

#125

Post by cubefox »

layer8 wrote: post #122
cubefox wrote: post #92

Earlier quoted context omitted.

Any normal die could also land on an edge.

It’s infinitely unlikely to do so, a set of measure zero.

Just as with the gömböc. Though the latter balances on only one unstable axis while a D6 die does so on 20 (12 edges and 8 vertices).

Re: A new pyramid-like shape always lands the same side up

#126

Post by stavros »

riffraff wrote: post #124
stavros wrote: post #119

Earlier quoted context omitted.

Huh, now I'm curious, what did the D2 look like?

Lenticoidal, I guess? I.e. remove the outer face of the cilinder by making the faces curved

Yeah, that was my thought as well, but that's also basically a D3 with a really small third edge, in practice. I was wondering whether there's some clever shape that actually is a D2, though maybe that's a Möbius strip in reality.

Re: A new pyramid-like shape always lands the same side up

#128

Post by close04 »

stavros wrote: post #126
riffraff wrote: post #124

Earlier quoted context omitted.

Lenticoidal, I guess? I.e. remove the outer face of the cilinder by making the faces curved

Yeah, that was my thought as well, but that's also basically a D3 with a really small third edge, in practice. I was wondering whether there's some clever shape that actually is a D2, though maybe that's a Möbius strip in reality.

> with a really small third edge

Doesn't every die have a bunch of edges or even vertices that aren't considered faces despite having a measurable width? As long as it's realistically impossible to land on that edge, I think it shouldn't count as a face.

Re: A new pyramid-like shape always lands the same side up

#130

Post by XCSme »

MPSimmons wrote: post #63
JKCalhoun wrote: post #43

Earlier quoted context omitted.

Wild prices for gömböcs on Amazon.

https://www.thingiverse.com/thing:1985100/files

Does it work when 3rd printed? How sensitive is it to infill options or infill density variations?
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