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A new pyramid-like shape always lands the same side up
- boznz 1y agomaybe they should build moon landers this shape :-)
- tgbugs 1y agoThat is indeed the example they mention in the paper https://arxiv.org/abs/2506.19244 https://arxiv.org/abs/2506.19244.
- orbisvicis 1y agoPer 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 1y ago[flagged]
- gerdesj 1y agoOr aeroplanes. Not sure where you put the wings. Why restrict yourself to the Moon?
- Cogito 1y agoRecent moonlanders have been having trouble landing on the moon. Some are just crashing, but tipping over after landing is a real problem too. Hence the joke above :)
- gerdesj 1y agoMars landers have also had a chequered history. I remember one NASA jobbie that had a US to metric units conversion issue and poor old Beagle 2 that got there, landed safely and then failed to deploy properly.
- weq 1y agoJust 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.
- emporas 1y agoThey could do that, but a regular gomboc would be totally fine. There are no rules for spaceships that their corners cannot be rounded. Maybe exoskeletons for turtles could be more useful. Turtles with their short legs, require the bottom of their shell to be totally flat, and a gomboc has no flat surface. Vehicles that drive on slopes could benefit from that as well.
- waste_monk 1y ago>There are no rules for spaceships that their corners cannot be rounded. Someone should write to UNOOSA and get this fixed up.
- nextaccountic 1y agoNote that a turtle's shell already approximate a Gömböc shape (the curved self-righting shape discovered by the same mathematician in the linked article) https://en.wikipedia.org/wiki/G%C3%B6mb%C3%B6c#Relation_to_animals https://en.wikipedia.org/wiki/G%C3%B6mb%C3%B6c#Relation_to_a... But yeah a specially designed exoskeleton could perform better, kinda like the prosthetics of Oscar Pistorious
- fruitplants 1y agoGábor Domokos (mentioned in the article) talked about this on one QI episode: https://www.youtube.com/watch?v=ggUHo1BgTak https://www.youtube.com/watch?v=ggUHo1BgTak
- voidUpdate 1y ago> There are no rules for spaceships that their corners cannot be rounded If the inside is pressurized, its even beneficial for it to be a rounded shape, since the sharp corners are more likely to fail
- ErigmolCt 1y ago"If tipped, will self-right" sounds like exactly the kind of feature you'd want on the Moon
- shdon 1y agoAnd for cows
- mihaaly 1y agoThey will only need to ensure that the pointy end does not penetrate the soft surface too much on decent, becoming an eternal pole.
- mosura 1y agoSomewhat 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.
- dyauspitr 1y agoYeah isn’t this just like those toys with a heavy bottom that always end up standing straight up.
- deleted 1y ago[deleted]
- lgeorget 1y agoThe main difference, and it matters a lot, is that all the surfaces are flat.
- tpurves 1y agoThat implies the interesting question though, which shape and mass distribution comes closest to, or would maximize relative uniformity?
- nick238 1y agoGiven 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.
- orbisvicis 1y agoDid they actual prove this?
- robinhouston 1y agoThey 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)
- devenson 1y agoA reminder that simple inventions are still possible.
- malnourish 1y agoSimple invention made possible by sophisticated precision manufacturing.
- Retr0id 1y agoYou could simulate this in software, or even reason about it on paper.
- GuB-42 1y agoI 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!
- adriand 1y agoIt's funny, I was wondering about the exact example of a bicycle a few days ago and ended up having a conversation with Claude about it (which, incidentally, made the same point you did). It struck me as remarkable (and still does) that this method of locomotion was always physically possible and yet was not discovered/invented until so recently. On its face, it seems like the most important invention that makes the bicycle possible is the wheel, which has been around for 6,000 years!
- xeonmc 1y agoReminded me of Gömböc[0]
- DerekL 1y agoMentioned in the article.
- Retr0id 1y agoIt'd be nice to see a 3d model with the centre of mass annotated
- Terr_ 1y agoWe 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 https://en.wikipedia.org/wiki/Centroid
- strangattractor 1y agoOMG It looks like a cat:)
- ChuckMcM 1y agoWorst 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.
- deleted 1y ago[deleted]
- Evidlo 1y ago> A structure like that would be useful as a tamper detector. Why does it need to be a polyhedron?
- ChuckMcM 1y agoI 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.
- nancysmith865 1y ago[flagged]
- cbsks 1y agoThe 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 https://en.wikipedia.org/wiki/G%C3%B6mb%C3%B6c Here's a 21 sided mono-monostatic polyhedra: https://arxiv.org/pdf/2103.13727v2 https://arxiv.org/pdf/2103.13727v2
- Y_Y 1y agoThat's not a Platonic solid. Come on, like.
- lynnharry 1y agoYeah. I tried to google what's Platonic solid and each face of a platonic solid has to be identical.
- peeters 1y agoIt's a meaningless distinction. A solid is defined by a 3D shape enclosed by a surface. It doesn't require uniform density. Just imagine that the sides of this surface are infinitesimally thin so as to be invisible and porous to air, and you've filled the definition. Don't like this answer, then just imagine the same thing but with an actual thin shell like mylar. It makes no difference.
- peeters 1y agoOops disregard this, by "has to be identical" I thought you were objecting to the non uniformity of the surface, not the incongruity of the sides' shapes, so that's where my comment was coming from. The incongruity of the sides certainly makes it not a Platonic Solid, though the article doesn't actually assert that it is. It just uses some terrible phrasing that's bound to mislead. Their words with my clarification for how it could be parsed in a factually accurate way: "A tetrahedron is the simplest Platonic solid (when it's a regular tetrahedron). Mathematicians have now made one (a tetrahedron, not a Platonic solid)...". It's a dumb phrasing, it's like saying "Tesla makes the world's fastest accelerating sports car. I bought one" and then revealing that the "one" refers to a Tesla Model 3, not the fastest accelerating sports car.
- kazinator 1y agoThis is categorically different from the Gömböc, because it doesn't have uniform density. Most of its mass is concentrated in the base plate.
- bennydony826 1y ago[flagged]
- Nevermark 1y ago> 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 1y agoIf 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.
- Nevermark 1y agoThat isn't true. Look at the pictures. It has the same outer shape, that is all that is required for the geometry. And for center of mass, you set the positions for the bars, any variations in their thickness, then size and place the flat facet, in order to achieve the same center of mass as for a filled uniform density object of the same geometry. As the article says: > carefully calibrated center of mass Unless an object has internal interactions, for purposes of center of mass you can achieve the uniform-density-equivalent any way you want. It won't change the behavior.
- gus_massa 1y ago> Unless an object has internal interactions, for purposes of center of mass you can achieve the uniform-density-equivalent any way you want. It won't change the behavior. That is true, but they are using a very heavy material for a small part and very light material for the other. So in this case the center of mass is almost on one of the faces of the polyhedron.
- pizzathyme 1y agoCouldn'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 1y agoA 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.
- Etheryte 1y agoNote: the GP comment didn't include the word "weighted" when I made my comment, their edit makes this comment look like nonsense.
- zuminator 1y agoThe article acknowledges that roly-poly toys have always worked, but in this case they were looking for polyhedra with entirely flat surfaces.
- MikeBenemorhbc 1y ago[flagged]
- tbeseda 1y agoSo, like my Vans? https://en.wikipedia.org/wiki/Vans_challenge https://en.wikipedia.org/wiki/Vans_challenge
- ErigmolCt 1y agoThe tetrahedron is basically the high-fashion Vans of the geometry world
- nancysmith865 1y ago[flagged]
- Trowter 1y agobabe wake up a new shape dropped
- bradleyy 1y agoI hope I can buy one of these at the next DragonCon, along side the stack of D20s I end up buying every year.
- yobid20 1y agoDoesnt 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 1y agoEvery single shot shows a finger releasing the model.
- yobid20 1y agoCan'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 1y agoA sphere is not a tetrahedron.
- dotancohen 1y agoYes, that is not challenging. Finding (and building) a tetrahedron is challenging.
- a_imho 1y agoSeveral gömböcs in action https://youtube.com/watch?v=xSdi51HSkIE https://youtube.com/watch?v=xSdi51HSkIE
- deleted 1y ago[deleted]
- WillPostForFood 1y agoJapan's next moon lander should be this shape.
- sly010 1y agoMath has a PR problem. The weight being non-uniform makes this a little unsurprising to a non-mathematician, it's a bit like a wire "sphere" with a weight attached on one side, but a low poly version. Giving it a "skin" would make this look more impressive.
- seniortaco 1y agoIt appears unsurprising because it is unsurprising.
- yonisto 1y agoSo cats are pyramids?
- kijin 1y agoLiquid pyramids that rearrange their own molecular structure in response to a gravitational field. They're like self-landing rockets, but cooler and cuter.
- m3kw9 1y agoGonna make a dice using this
- eggy 1y agoGreat article! The excitement kind of ebbed early on with seeing the video and realizing it had a plate/weight on one face. "A few years later, the duo answered their own question, showing that this uniform monostable tetrahedron wasn’t possible. But what if you were allowed to distribute its weight unevenly?" But the article progressed and mentioned John Conway, I was back!
- K0balt 1y agoMade me think of lander design. Recent efforts seem to have created a shape that always ends up on its side? XD
- globular-toast 1y agoInitially I thought it was unimpressive because of the plate. But then I thought about it a bit: a regular tetrahedron wouldn't do that no matter how heavy one of the faces was.
- Silent_deport 1y ago[dead]
- sahil_sharma0 1y ago[dead]
- ErigmolCt 1y agoConway casually tossing out the idea, and then 60 years later someone actually builds it... that's peak math storytelling.
- KevinCarbonara 1y agoReminds me of when Mendeleev argued that an element that had just been discovered was wrong, and that the guy who discovered it didn't know what he was talking about, because Mendeleev had already imagined that same element, and it had different properties. Mendeleev turned out to be right.
- cbogie 1y agoa skateboard
- ColinWright 1y agoThe 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 https://arxiv.org/abs/2506.19244 The content in HTML is here: https://arxiv.org/html/2506.19244v1 https://arxiv.org/html/2506.19244v1
- s4mbh4 1y agoWould be awesome to see some pictures!
- ColinWright 1y agoI've knocked up a quick page: https://www.solipsys.co.uk/ZimExpt/MonostableTetrahedron.html https://www.solipsys.co.uk/ZimExpt/MonostableTetrahedron.htm...
- gus_massa 1y agoI was expecting to see the photos, but the jpg are linked there instead of visible. IIRC you were using a self-made CMS for your blog, with more support for math formulas. Does it not allow images?
- ColinWright 1y agoEveryone complains about how crap my website is, so in this case I've just exported a page from my internal zim-wiki. Yes, it can have photos, but it doesn't give any control over sizing or positioning, so I'm providing links for people to click through to. It's the middle of my working day and I'm in the middle of meetings, so I don't have time to do anything more right now.
- 1y ago
- hashstring 1y agoNice, would be a good update for turtles & PBJ sandwiches.
- ourmandave 1y agoFrom just the headline, they're describing a cat.
- Elaris 1y agoWhat really gets me is how something that looks off balance ends up being super stable. This shape makes you rethink what balance actually means. It's not just about equal forces. It almost feels like the shape knows where it wants to land every time.
- seniortaco 1y agoI wouldn't really call this a "shape" since the highly manipulated center of mass is what is actually doing the work here. I would call this an object or rigid body.
- naikrovek 1y agoI agree with you.
- hinkley 1y agoIt’s both. To work you need a polyhedron constructed of a series of polygons, here triangles, and one of those triangles has to have its center of mass outside the base of the object in all orientations. Otherwise the weight will pin it down instead of tilt it over. That’s why in the one orientation it tips back before tipping sideways: the center of mass is inside the footprint of right edge of the tetrahedron but not the back edge. So it tips back, which then narrows the base enough for it to tip over to the right and settle.
- jrowen 1y agoThe article does a good job of explaining that it's still a non-trivial problem even if you are allowed to distribute the weight unevenly, but I do agree that what is happening here is much more specific than a "shape," which is simply geometry without any density information. Put another way, most things precisely constructed with that same exact shape (of the outer hull, which is usually what is meant by shape) would not exhibit this property.
- kamel3d 1y agoA ball that has a weight attached to one point from the inside would always land on that side, it's the same thing, right?
- Vvector 1y agoLast time I checked, spheres are shapes. But the article references a "pyramid-like shape"
- mannyv 1y agoMaybe they should use this shape for interplanetary landers. Oop, they mentioned that in the article.
- deleted 1y ago[deleted]
- scubadude 1y agoGreat for dnd dice, crits errytime