[HN Gopher] A new pyramid-like shape always lands the same side up
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A new pyramid-like shape always lands the same side up
Author : robinhouston
Score : 184 points
Date : 2025-06-25 20:01 UTC (2 hours ago)
(HTM) web link (www.quantamagazine.org)
(TXT) w3m dump (www.quantamagazine.org)
| boznz wrote:
| maybe they should build moon landers this shape :-)
| tgbugs wrote:
| That is indeed the example they mention in the paper
| https://arxiv.org/abs/2506.19244.
| orbisvicis wrote:
| 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.
| mosura wrote:
| 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 wrote:
| That implies the interesting question though, which shape and
| mass distribution comes closest to, or would maximize relative
| uniformity?
| orbisvicis wrote:
| Did they actual prove this?
| robinhouston wrote:
| 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 wrote:
| 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.
| robinhouston wrote:
| It sounds as though you're talking about the solution to
| part (b) as given in that reference. Have a look at the
| solution to part (a) by Michael Goldberg, which I think
| does prove that a homogeneous tetrahedron must rest
| stably on at least two of its faces. The proof is short
| enough to post here in its entirety:
|
| > A tetrahedron is always stable when resting on the face
| nearest to the center of gravity (C.G.) since it can have
| no lower potential. The orthogonal projection of the C.G.
| onto this base will always lie within this base. Project
| the apex V to V' onto this base as well as the edges.
| Then, the projection of the C.G. will lie within one of
| the projected triangles or on one of the projected edges.
| If it lies within a projected triangle, then a
| perpendicular from the C.G. to the corresponding face
| will meet within the face making it another stable face.
| If it lies on a projected edge, then both corresponding
| faces are stable faces.
| dyauspitr wrote:
| Yeah isn't this just like those toys with a heavy bottom that
| always end up standing straight up.
| lgeorget wrote:
| The main difference, and it matters a lot, is that all the
| surfaces are flat.
| devenson wrote:
| A reminder that simple inventions are still possible.
| malnourish wrote:
| Simple invention made possible by sophisticated precision
| manufacturing.
| Retr0id wrote:
| You could simulate this in software, or even reason about it
| on paper.
| GuB-42 wrote:
| I think it is a very underestimated aspect of how "simple"
| inventions came out so late.
|
| An interesting one is the bicycle. The bicycle we all know
| (safety bicycle) is deceivingly advanced technology, with
| pneumatic tires, metal tube frame, chain and sprocket, etc...
| there is no way it could have been done much earlier. It
| needs precision manufacturing as well as strong and
| lightweight materials for such a "simple" idea to make sense.
|
| It also works for science, for example, general relativity
| would have never been discovered if it wasn't for precise
| measurements as the problem with Newtonian gravity would have
| never been apparent. And precise measurement requires precise
| instrument, which require precise manufacturing, which
| require good materials, etc...
|
| For this pyramid, not only the physical part required
| advanced manufacturing, but they did a computer search for
| the shape, and a computer is the ultimate precision
| manufacturing, we are working at the atom level here!
| xeonmc wrote:
| Reminded me of Gomboc[0]
| DerekL wrote:
| Mentioned in the article.
| Retr0id wrote:
| It'd be nice to see a 3d model with the centre of mass annotated
| Terr_ wrote:
| 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.
|
| [0] https://en.wikipedia.org/wiki/Centroid
| strangattractor wrote:
| OMG It looks like a cat:)
| neilv wrote:
| https://en.wikipedia.org/wiki/Buttered_cat_paradox
| ChuckMcM wrote:
| 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.
| Evidlo wrote:
| > A structure like that would be useful as a tamper detector.
|
| Why does it need to be a polyhedron?
| ChuckMcM wrote:
| 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.
| cbsks wrote:
| The keyword is "mono-monostatic", and the Gomboc 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 wrote:
| Okay, I love this so much :-). Thanks for that.
| ortusdux wrote:
| 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.
| gerdesj wrote:
| 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)
| Y_Y wrote:
| That's not a Platonic solid. Come on, like.
| kazinator wrote:
| This is categorically different from the Gomboc, because it
| doesn't have uniform density. Most of its mass is concentrated in
| the base plate.
| Nevermark wrote:
| > 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.
| JKCalhoun wrote:
| Wild prices for gombocs on Amazon.
| pizzathyme wrote:
| 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?
| Etheryte wrote:
| 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.
| zuminator wrote:
| The article acknowledges that roly-poly toys have always
| worked, but in this case they were looking for polyhedra with
| entirely flat surfaces.
| tbeseda wrote:
| So, like my Vans?
|
| https://en.wikipedia.org/wiki/Vans_challenge
| Trowter wrote:
| babe wake up a new shape dropped
| bradleyy wrote:
| I hope I can buy one of these at the next DragonCon, along side
| the stack of D20s I end up buying every year.
| yobid20 wrote:
| 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 wrote:
| [delayed]
| yobid20 wrote:
| Can't you just use a sphere with a small single flat side made
| out of heavier material? That would only ever come to rest the
| same way every single time.
| mreid wrote:
| A sphere is not a tetrahedron.
| dotancohen wrote:
| Yes, that is not challenging. Finding (and building) a
| tetrahedron is challenging.
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