A new pyramid-like shape always lands the same side up
70 comments
·June 25, 2025ChuckMcM
ortusdux
You jest, but I knew a DND player with a dice addicting that loved showing off his D-1 Mobius strip dice - https://www.awesomedice.com/products/awd101?variant=45578687...
For some reason he did not like my suggestion that he get a #1 billard ball.
robocat
That's like saying a donut only has one side.
The linked die seems similar to this: https://cults3d.com/en/3d-model/game/d1-one-sided-die which seems adjacent to a Möbius strip but kinda isn't because the loop is not made of a two sided flat strip. https://wikipedia.org/wiki/M%C3%B6bius_strip
Might be an Umbilic torus: https://wikipedia.org/wiki/Umbilic_torus
The word side is unclear.
gerdesj
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)
thaumasiotes
> Love it - any sphere will do.
That's basically what the link shows. A Möbius strip is interesting in that it is a two-dimensional surface with one side. But the product is three-dimensional, and has rounded edges. By that standard, any other die is also a d1. The surface of an ordinary d6 has two sides - but all six faces that you read from are on the same one of them.
thaumasiotes
> the DM/GM could throw it at a player for effect without braining them!
If you're prepared to run over to wherever it ended up after that, sure.
I learned to juggle with ping pong balls. Their extreme lightness isn't an advantage. One of the most common problems you have when learning to juggle is that two balls will collide. When that happens with ping pong balls, they'll fly right across the room.
hammock
Or any mobius strip
MPSimmons
I've always seen a D1 as a bingo ball...
cbsks
The keyword is "mono-monostatic", and the Gömböc is an example of a non-polyhedra one: https://en.wikipedia.org/wiki/G%C3%B6mb%C3%B6c
Here's a 21 sided mono-monostatic polyhedra: https://arxiv.org/pdf/2103.13727v2
ChuckMcM
Okay, I love this so much :-). Thanks for that.
jayd16
I imagine a dowel that is easily tipped over fits your description but I must be missing something.
gus_massa
A solid tall cone is quite similar to what you want. I guess it can be tweaked to get a polyhedra.
MPSimmons
A weeble-wobble
Evidlo
> A structure like that would be useful as a tamper detector.
Why does it need to be a polyhedron?
ChuckMcM
I was thinking exactly two stable states. Presumably you could have a sphere with the light end and heavy end having flats on them which might work as well. The tamper requirement I've worked with in the past needs strong guarantees about exactly two states[1] "not tampered" and "tampered". In any situation you'd need to ensure that the transition from one state to the other was always possible.
That was where my mind went when thinking about the article.
[1] The spec in question specifically did not allow for the situation of being in one state, and not being in that one state as the two states. Which had to do about traceability.
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nancysmith865
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boznz
maybe they should build moon landers this shape :-)
tgbugs
That is indeed the example they mention in the paper https://arxiv.org/abs/2506.19244.
gerdesj
Or aeroplanes. Not sure where you put the wings.
Why restrict yourself to the Moon?
orbisvicis
Per the article that's what they're working on, but it probably won't be based on tetrahedrons considering the density distribution. Might have curved surfaces.
bennydony826
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weq
Just need to apply this to a drone, and we would be one step closer to skynet. The props could retract into the body when it detects a collision or a fall.
kazinator
This is categorically different from the Gömböc, because it doesn't have uniform density. Most of its mass is concentrated in the base plate.
Nevermark
> This tetrahedron, which is mostly hollow and has a carefully calibrated center of mass
Uniform density isn't an issue for rigid bodies.
If you make sure the center of mass is in the same place, it will behave the same way.
kazinator
If the constraints are that an object has to be of uniform density, convex, and not containing any voids, then you cannot choose where its centre of mass will be, other than by changing it shape.
bennydony826
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a_imho
Several gömböcs in action https://youtube.com/watch?v=xSdi51HSkIE
bradleyy
I hope I can buy one of these at the next DragonCon, along side the stack of D20s I end up buying every year.
tbeseda
So, like my Vans?
mosura
Somewhat disappointing that it won’t work with uniform density. More surprising it needed such massive variation in density and couldn’t just be 3d printed from one material with holes in.
tpurves
That implies the interesting question though, which shape and mass distribution comes closest to, or would maximize relative uniformity?
nick238
Given they needed to use a tenuous carbon fiber skeleton and tungsten carbide plate, and a stray glob of glue throws off the balance...seems tough.
dyauspitr
Yeah isn’t this just like those toys with a heavy bottom that always end up standing straight up.
lgeorget
The main difference, and it matters a lot, is that all the surfaces are flat.
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orbisvicis
Did they actual prove this?
robinhouston
They didn't need to, because it was proven in 1969 (J. H. Conway and R. K. Guy, _Stability of polyhedra_, SIAM Rev. 11, 78–82)
zuminator
That article doesn't prove what you say that it does. It just proves because a perpetuum mobile is impossible, it is trivial that a polyhedron must always eventually come to rest on one face. It doesn't assert that the face-down face is always the same face (unistable/monostable). It goes on to query whether or not a uniformly dense object can be constructed so as to be unistable, although if I understand correctly Guy himself had already constructed a 19-faced one in 1968 and knew the answer to be true.
SonomaSays
[dead]
Retr0id
It'd be nice to see a 3d model with the centre of mass annotated
Terr_
We can safely assume the center of mass is the center [0] of the solid tungsten-carbide triangle face... or at least so very close that the difference wouldn't be perceptible.
pizzathyme
Couldn't you achieve this same result with a ball that has one weighted flat side?
And then if it needs to be more polygonal, just reduce the vertices?
zuminator
The article acknowledges that roly-poly toys have always worked, but in this case they were looking for polyhedra with entirely flat surfaces.
Etheryte
A ball that has one flat side can land on two sides: the round side and the flat side. You can easily verify this by cutting an apple in half and putting one half flat side down and the other flat side up.
yobid20
Doesnt the video start out with laying on a different side then after it flips? Doesnt that by definition mean that its landing on different sides?
jamesgeck0
Every single shot shows a finger releasing the model.
null
Worst D-4 ever! But more seriously, I wonder how closely you could get to an non-uniform mass polyhedra which had 'knife edge' type balance. Which is to say;
1) Construct a polyhedra with uneven weight distribution which is stable on exactly two faces.
2) Make one of those faces much more stable than the other, so if it is on the limited stability face and disturbed, it will switch to the high stability face.
A structure like that would be useful as a tamper detector.