Hexagons Are NotSoGreatAgons

[@ConHathy]

4:52 I should have mentioned but you only need all of the extra members if you don’t add another joint in the middle. If you add a joint in the middle then you just need the 6 equilateral triangles to keep it stable.

[@ronweber4508]

I’ve been trying to get an answer to my question, maybe you can help me? My idea, hypothetical. Is there any scenario where…? A person could have large tall cylinder that can withstand both a vacuum and pressure, with a valve at the bottom and top of this vessel. Setting above but next to an open reservoir of water. Fill the vessel with water just below the valve at the top of the barrel. From the valve at the top of the barrel connect a small pipe that reaches into the open water reservoir. From the bottom valve connect another pipe that reaches out… say 12’, but staying above the top of the water in the reservoir. Is there any scenario in this kind of setup where, when the valve in the bottom of the closed vessel, with the weight of the water in the barrel decrease the atmospheric pressure artificially in the top of the tank, to overwhelm the atmospheric pressure of the reservoir of water and the water weight in the smaller tube connected to the upper valve, So that when the upper valve is opened the water would flow up the tube and into the top of the sealed vessel?

[@X4R2]

In the 6 equilateral triangle arrangement, could you actually remove one member shared by two of the equilateral triangles and the structure would still be statically determinant? Then there would be 4 equilateral triangles and a rhombus, but three of the rhombus' vertices would be fixed.

[@williammorris1763]

I was literally imagining that rocket video before you said it. Algo go burrr.

[@oliverdowning1543]

​@@X4R2 possibly except that that would have the possibility of the corner flipping into itself because only fixing the of the corners creates a bistable configuration which is fine if there's not give in the beams but as soon as there is you have issues. Ultimately it makes it more susceptible to bucking on that corner if you have a force from the corner to the centre joint of the hexagon which isn't ideal.

[@AnttiAlajuuma]

@@ronweber4508 It's been a while since you posted this question but nobody seems to have answered it so here's my two cents: Short answer no, long answer yes, with certain conditions. The water in the small pipe going to the top of the cylinder would not flow all the way up into the cylinder because the same gravity that affects the water in the cylinder affects also the water in the small pipe. If you open both of the valves the pressure at the top of the cylinder would lower and it would suck up water into the small pipe but only until the level of the water in the small pipe matches the level of the water in the cylinder. If we start nitpicking we could make the top pipe very small. The capillary force would cause the water in the pipe rise higher than in the cylinder. Even all the way into the cylinder. Capillary force is caused by the surface tension of the water. Water is attracted to many surfaces and wants spread on them even climbing up them slightly. (watch closely at the edges of the water in a glass of water) In a very thin tube the capillary force overcomes the gravity. This is the way how water rises up in tree trunks all the way up to the leaves. It's also how they take a blood sample from you by squeezing out a small drop of blood and touching it with a thin glass tube so the blood just fills the tube "automatically". But in this scenario the water rises up into the top of the cylinder because of the capillary force and not because of the low pressure at the top. Although the pressure difference certainly helps. If you place the cylinder and the bottom pipe next to the open reservoir but below the level of the water in the reservoir, opening the valves would suck up the water into the small pipe and into the cylinder. The cylinder and the pipes would act as a siphon and would create a flow of water from the reservoir into wherever the the lower pipe ends ups.

[@JustAlfy]

Now this is the type of youtube drama between youtubers i like to see

[@negativedisplay]

@arandomgamer3088Don’t even try to compare this to SSSniperwolf

[@orangecitrus8056]

virgin dream v gumball chad cgp v con hathy

[@TheBenenene10]

You'll want to check out the feud of ElectroBoom and Steve Mould over the Mould Effect a few years back

[@ImGoingToLickYou]

Yum

[@Monkeymario.]

Yum

[@Albtraum_TDDC]

- Can you guess where this goes? - It goes in the square hole...

[@angusmacchesney5810]

Where does the semicircle go? That’s right, the square hole

[@ImGoingToLickYou]

Gulp

[@Albtraum_TDDC]

@user-yb5cn3np5q I'm just relieved other people share my trauma :P

[@__________________________hi52]

Where does the cylinder go?

[@__________________________hi52]

Correct! The square hole

[@MilkyWayWasTaken]

CGP Grey: Hexagons are the Bestagons! Con Hathy: Triangles are the Bestangles!

[@thundergamergd]

Squares are the bares

[@JaymcJefty]

@@thundergamergdcircles are the bercles

[@eclassiskandar8190]

@@JaymcJefty cones are the bones

[@Spinex0196]

squares are the best heirs

[@Violence-JoséRicardo]

​@@eclassiskandar8190 this actually goes hard though

[@athertongraham8660]

Things are heating up in the shape fandom

[@TheCoriKat]

The polygon fandom

[@ianmorgadovillasenor215]

​@@TheCoriKatcan't wait for the polyhedra update!

[@TheCoriKat]

@@ianmorgadovillasenor215 I'm super hyped for the fractal DLC coming out February!

[@eshelsh1905]

@TheCoriKat it was supposed to go out in October but the keep refining the details…

[@londonalicante]

Chemist turned engineer here. Hexagons ARE the best way to fill the space between 2 strong sheets in a honeycomb for precisely the reason CGP mentioned: they fill an area with the least amount of length. However this is only true for a general purpose (isotropic) honeycomb. If you require more strength in one direction than the other, then a rectangular grid is best per the rocket example you gave. If you have only one sheet, then the other side is subject to buckling, so the best isotropic grid is the triangle one that you showed. Hexagons are essentially useless for making a rigid structure from beams - for that you obviously need triangles. But if you want to make a 2D atomic sheet it has to be hexagons. Bonds spread out to fill 3d space due to VSEPR. An atom with 3 bonds (and no spare electrons) will be flat with 120 angles as in boron trifluoride (Graphene is a bit more complex, there is a 4th electron on each atom but it is used in a delocalised electron cloud unlike the other 3 which are paired with neighbours into 3 discrete bonds.) if you have more than 3 bonds they make a 3d structure, for example 4 bonds form a tetrahedron as in methane or diamond and 6 bonds form right angles like a cube lattice, as in sodium chloride (ionic bonds) or sulphur hexafluoride (covalent bonds.) Molecules containing an atom with 4 bonds in the same plane do exist, but the atom in question is always a fairly heavy one with a total of 6 electron pairs to maintain that cube-like geometry (the electron pairs that are not used in bonding occupy the poles of the six-sided cube and therefore push the 4 bonds into a flat configuration around the equator of the atom.) To my knowledge nobody has made a flat sheet of atoms in this way - the electron pairs that are not used in bonding (and their corresponding orbitals) would leave the molecule vulnerable to being attacked chemically, even by itself. If you are stacking long thin objects, a stack of hexagonal prisms is stronger / more stable than square prisms or triangular prisms, because it doesn't have shear planes. A fistful of hexagonal pencils feels quite rigid, but with square or triangular prisms they would tend to slide across each other.

[@felixu95]

You're right if you restrict your shape selection to regular polygons, and if your core/filler is purely for volumetric (aka non-structural) reasons. However, break those two assumptions for your application and it may no longer be true that hexagons offer the best mass/path length for the situation. For example, an application with negligible radial loads will be theoretically better served with only axially-aligned members, minus a couple radially aligned segments to reduce twist.

[@Gameknight2169]

"A fistful of hexagonal pencils feels quite rigid, but with square or triangular prisms they would tend to slide across each other." That's an excellent analogy.

[@londonalicante]

@@felixu95 Isotropic means "equal properties (in this case strength) in all directions." What you are describing is a non-isotropic case. Actually a hexagon grid isn't perfectly isotropic (properties parallel and perpendicular to the sides vary slightly, cycling every 60 degrees) but is more isotropic than a square grid (properties at 0 and 45 degrees vary, cycling every 90 degrees.) I already accepted OP's point that another grid is better if you want more strength in one direction than another, such as the rectangular grid in OP's rocket example. Perfect hexagon grids are rare in practice both because they're not always the best solution, and (as OP mentioned) because of manufacturing. The hexagonal packing insided IKEA table tops is made from strips of card bonded together, for example, and is therefore twice as thick in one direction than in the other two.

[@londonalicante]

@@Joe-sg9ll Bees use hexagons because it optimises storage volume. Actually the bottoms of the cells are made of three rhombuses with diagonals in the ratio sqrt(2):1 (like the corners of a shape called a rhombic dodecahedron) as this further optimises storage volume (it means the front and back sides are offset from each other though.) Bees also seal most of the cells of the honeycomb, and in that state, the structure is also optimised.

[@ravener96]

thats.... an extreamly narrow area of application. we happen to need that quite a lot, but it's still an extremely weak shape in the plane.

[@andrewkuebler4335]

Ah yes, the ever vile feud between physics and applied engineering.

[@rkond]

I don’t believe you missed the opportunity to call squares tetragons.

[@SirPhysics]

And trigons. We must always push for consistency in our nomenclature. You can't have triangles and hexagons. Either trigons and hexagons or triangle and hexangles.

[@SaHaRaSquad]

And the rectangles rectagons

[@angeldude101]

@@SaHaRaSquad Rectangles are nothing more than right tetragons. Rhombuses meanwhile are equilateral tetragons, and squares are right _and_ equilateral tetragons, or just regular tetragons for short. (Worth noting however that squares and retangles are only right tetragons in euclidean space.)

[@SpydersByte]

@@SirPhysics Trigon? Dont mention Trigon dude, Raven from the Teen Titans might hear you talking about her dad.

[@grey5751]

​@nisonatic i believe i hate this thing you've said.

[@sIosha]

It's been awhile since I watched Grey's video, but essentially bees use hexagons because the shape is efficient and engineers use triangles because the shape is strong. The shapes are used for different applications. Great.

[@youkofoxy]

Triangles and engineers. The best love story.

[@chem-spider6975]

Good thing it's not a love triangle.

[@1Worm_antifurry]

Holy fuck it's youkofoxy

[@amagicalbeing7427]

Ford and bill cipher

[@dsmith530]

The only reason bees use hexagons is because they’re circles without the packing density losses. They’re literally just simplified circles with flat sides so there’s no dead space. They’re a packing density optimized circle. It had nothing to do with strength, and everything to do with the efficient use of material to subdivide a given volume

[@ultimatedude5686]

In fact I believe bees actually make their hives out of circles which naturally deform into hexagons because they are the most efficient shape.

[@TXA-TXAT]

when the fuck am i gonna use hexagons for that reason

[@theapexsurvivor9538]

​@@TXA-TXATwhen you can only make roughly cylindrical shapes and need to pack a lot of fluid into the smallest volume possible.

[@theapexsurvivor9538]

​@@ultimatedude5686yep, more or less. Bees shape their honeycomb using their abdomen, which is roughly circular. As the hive heats and cools the wax melts and hardens. Due to most of the combs being filled and/or fully supported, they don't collapse, but they do fuse. Due to the fact that hexpacking is the most space efficient packing for cylindrical tubes this means that the combs create flats on the six sides where they meet and bulge towards the "corners" to maintain their volume. So they actually just form the appropriate N-gon to tile their packing formation.

[@user-tl4bg3ci3g]

and?

[@Reactorjam]

I hope cgp gray sees this Even if the hexagon isn’t the bestagon it still looks good

[@reelrook3044]

They are the Coolest of gons.

[@mookiemorjax]

Good thing they are, in fact, the bestagons!

[@junovzla]

it's the bestlookingagon

[@JoaoVitorBarg]

I hope so

[@thewatcherinthecloud]

Appeal: Triangles don't count because they aren't "-gons", neither do squares because the quadrilateral family is their own mess. Ergo, hexagon still bestagon.

[@ottekitfun9626]

Hey, chemist here. I want to add some stuff because I think this video misunderstand the foundation of CGP Greys video. Hexagonal structures are great because they act like triangles in a planar 2D structure without wasting needless material on actual triangles. However, as soon as we go into 3D space, we need a bunch more information. In nature there are 2 forms of structures that form in 3D space. Cubic, also called octahedral due to its 8 corners, and tetrahedral, which is due to 4 corners. Tetrahedral is, of course, 4 triangles in 3D space. These two types sometimes mix as pyramidal (square plane with 4 triangles), bipyramidal, etc. However, due to hexagonals innate property of "acting like triangles without wasting needless space or energy", some inorganic, or organic, compounds form natural hexagonal crystaline structures, bonded together between triangles. These are often tetrahedral cordinated crystaline structures, whereas the ordinary cubic crystaline structure is formed through octahedral cordinated compounds (this is inorganic chemistry). However, all this is completely irrelevant. CGP Grey already did mention most of the points of "square being X" and "Triangles being Y" in his video. His point was that Hexagonal structures where the only polygon that could cover a blank space without leaving gaps while maximizing the ratio between area of each hexagon and the surface of each hexagon. This also works in physics. The reason why hexagons are not used in structural engineering, but that we use triangles instead, is because of pressure differentials within the structure compared to outside. Hexagons minimize the material used for maximum space while holding structural integrity in a packed space. Cells form hexagons. Bee-hive combs, flowers, eyes, etc, all form hexagons because of this differential. The reason why this tidbit isnt useful in construction, is because you dont have a pressure from within. You want the structure to withstand force from the outside without additional force within. So you use triangles instead, which is what hexagons are derived from. Hexagons gets their superb distribution of forces from the triangle. Triangles having the 60 degree angles to form equal distribution of force between 3 equidistant fixture points. This is great for withstanding pressure from outside. Hexagons are great at distributing force from both within and from outside.

[@XatxiFly]

Thank you, much needed missing context that I was hoping to see in this video. CGP Grey never even called them "the strongest shape."

[@1forge2rulethemall88]

May we never forget the underappreciated 3rd best shape the square/rectangle, sure its not the best, but its pretty good, and easy to make. Its the Ok-agon

[@thezipcreator]

squares are the best because they're easiest to implement in code

[@chaos.corner]

It's no accident that it's everywhere.

[@bramvanduijn8086]

@@thezipcreator Oh? In what context? You'd think of the flat shapes the cirlce is easiest to implement since it only has one variable: radius. A square has four sides and four angles, which luckily you can compress to one side and one angle as long as you store the shape identifier as well, so that's still two variables more than a circle. Not to mention orientation in any n-dimensional reference frame where n >=2 becomes a whole thing with squares that it simply isn't with circles. Circle: Distance? Distance to centre minus radius. Collision? Distance to centre minus radius. End of shape? Distance to centre plus radius. Depth? Twice the radius. Square: Distance? Depends on the angle. Collision? Depends on the angle and rotation speed, if any. End of shape? Again, it depends. Depth? same issue.

[@thezipcreator]

@@bramvanduijn8086 rendering squares is easier (with circles you have to pass a bunch of points of the form [centerx+cosθ, centery+sinθ], with squares you can just pass 4 points), collision with AABBs is basically the same difficulty as spheres (although you are right that if a square is rotated it's much harder). also if your entire world is a grid (such as in strategy games), you don't even need to worry about that; making a square grid is just easier than making a hexagonal one (although not by enough that it matters, probably. idk I'm just a lazy developer).

[@BetaKeja]

@@thezipcreator easiest in a rectangular coordinate system. Which is most common, so yeah fair enough. 😛

[@yoanngrudzien2588]

Your video is really cool and interesting, however, I returned to the video Hexagons are the bestagons, and at no point does CGP Grey say that hexagons are the strongest shape. He speaks about how great they are at being able to tile the plane, and how strong they are compared to how little material they require when building, but he never says they are the strongest shape. Even when he speaks about graphene, he says that it is the strongest known material, and he says that it is made of hexagons, and that it does make graphene pretty light and sturdy at the same time, but he doesn't say that hexagons are the strongest shape. The closest he goes to saying something like that is "hexagons are strongagons", but even then, not "THE strongagon". The Order therefore declares you a heretic, for Hexagons are the bestagons.

[@andrewpeachey5416]

But hexagons are the bestagons. I joined the cult, sold my soul and pledged allegiance to the almighty hexagonal perfection. They must be the bestagons. 😩

[@Nugcon]

heretics!

[@SpahGaming]

@@Joe-sg9ll i refute that!

[@AJMansfield1]

Hexagons are the worstagons.

[@the_greyster]

Bro who uses that emoji 💀

[@beaclaster]

​@@Nugconhexetic

[@Eeatch]

As a person who studied construction in a university i think it's a shame teachers didn't properly explained this as good as you did. Wanted me to calculate loads at i-beams etc. without explaining this basic crusial concepts. I might be a bad student if i couldn't think of it myself in a thought experiment, but for sure this would be a good ground to a harder stuff. And it seems like i am not the only person who complain about the education system. Definitely enjoyed watching it!

[@squfucs]

0:28 Correct, I do watch CGP Grey and I saw that video. Actually your thumbnail decision was perfect, it pretty much immediately encapsulates the issue. Thanks for the vid bro, I'm gonna sub now.

[@whatthefunction9140]

a hexagon is just 4 triangles

[@Reactorjam]

6*

[@Reactorjam]

Oh I see what your talking about but it’s 6 IF we are talking about a triagle equal sides

[@dusker-nd2cf]

In that case triangles are just broken up hexagons.

[@unknowntimelord9557]

Ah yes... a triangle is just 3 triangles

[@LukeMlsna]

4 triangles is just 12 triangles

[@kaidwyer]

I guess hexagons are good for webbing 2D lattices where there is intrinsic repulsion between nodes, such as in graphene or some kind of “tensegrity net” that uses cord/cable for internal triangles and a rigid material for the hexagons.

[@omgitscake8933]

this is really interesting, i never really understood why some shapes are so much better than others, but this explains a lot! I guess diffirent shapes are great at handling specific directions of pressure, but triangles are by far the most usefull, since they can handle any direction. Circles are a funny one i think, since (from my understanding) they're the best at handling pressure from all directions simultaniously, like atmospheric pressure. But if the pressure is focused, if you were to try and stab one, or a set of circles, it'd be way weaker than triangles.

[@dranorter]

It'd be cool to see a really simplistic set of physics sims try and demonstrate the strongest shape against stabbing, strongest shape against atmospheric pressure, strongest shape against gravity, etc. etc.

[@thatyougoon1785]

you are entirely ignoring that hexagonal tesselations and triangular tesselations are duals of one-another. Depending on the perspective of a problem, the answer can either be a triangular tesselation or a hexagonal tesselation, as they are just the sides of the same coin in essense. So the main question is, when is the square tesselation better than the triangular/hexagonal tesselation. I am way more obsessed with this topic than I'd like to admid and in all my research into this topic, there has neve been a problem to which squares are the optimal solution compared to either the hexagon or triangle.

[@dranorter]

I'm surprised you didn't mention the relatively low surface area of the hexagon fill in the paneling. They're closer to circular so they reduce the amount of materials compared with a triangular mesh -- yet another way in which the hexagon is the cheapagon. Bees use hexagons (well, actually they use halved rhombic dodecahedra) because it minimizes the amount of beeswax needed.

[@BalderOdinson]

The more pictures of hives I look at, the more I'm convinced they actually use circular tubes that are hexpacked together. If they're hexagons, the corners sure are beveled to hell!

[@EduardoEscarez]

@@BalderOdinson You're right, bees build the tubes of the beehive in a circular shape. The trick is that the wax itself keeps rearranging itself due to the heat of the hive, so it ends to stick together with the walls of the neighboring cells and makes the hexagons. But the idea of bees making the polygons is a myth, is just a quirk of the material of the hive.

[@bugjams]

​@@EduardoEscarez "The idea that humans melt metal themselves is a myth, it's just a quirk of the tools and materials they use." I mean, come on. Let the bees have their fame. Maybe they still _intend_ to make hexagons, they simply know that circles will mold themselves into hexagons, so really they're saving energy! :P

[@andrewmirror4611]

Rhombic dodecahedra aren't the best volume to surface area ratio either

[@coryzilligen790]

Of course the bees are actually creating circular tubes -- they're making them with their own abdomens, which are roughly circular in cross-section.

[@appa609]

There's no such thing as "the strongest shape" broadly. In some cases, spheres are optimal. In some cases tubes are optimal. And sometimes it's a hexagonal lattice. It depends entirely on context and constraints.

[@spectralstriker]

Spheres are optimal... when you need something to roll... like a ball bearing. Spheres are not as physically strong as triangles and are far more prone to pressure, no matter what material you make them out of. You can, in fact, say what shape is 'the strongest' since strength is a characteristic and not a descriptor within material sciences. Strength is "the ability of a material to withstand compression, tension and sheer." Triangles are much better at all three of these things compare to other shape no matter what you put them through. This isn't to say they are better suited for every task, but they are without a shadow of a doubt the strongest shape.

[@simsom4343]

Tbf, I think one of CGPs actual points (outside the jokes) was that hexagons are so good precisely because they have triangles easily in them (compared to triangles in squares I mean) Like essentially in triangle sheets vs hexagon sheets, the only difference is extra joints in each hexagon (to make it triangles). Compared to a square sheet that uses its own geometry entirely

[@someweeb3650]

With squares it's just that you need to use right triangles, which from most bridges we can see isn't as efficient as tiling equilaterals, which tile into hexagons

[@jhuyt-]

So triagons are the bestagons

[@livedandletdie]

Add 2 Triangles, to form a square, repeat 6 times, join these squares to each other in a t and then join the edges together. Cut the newfound cube along it's 3 dimensional diameter and it's cross section is a hexagon.

[@EdKolis]

Triangle Man, Triangle Man, Triangle Man hates Hexagon Man, they get in a fight, Triangle wins...

[@WisdomRanger]

@simsom4343 I am of the pro-CGP and pro-hexagon persuasion so keep that in mind when you read this. You're moving the goal posts in an apologist manner. This video presents valid criticisms of the Holy Hexagon Bestagon. Hexagon = bestagon is no more than a faith based fandom based on a decent, but incomplete/not fully incorrect explanation. As with any faith based belief, it will not stand up to strict scrutiny, empiricism, and reason. Faith based beliefs can be cool and useful, but I would not lean too hard/center my life/center my personality around anything so flimsy as a faith based system.

[@SarahC2]

1:00 Do NOT buckle your member by applying pressure to both ends! I think we've all learned something new today.

[@jdotoz]

That's why I design all my bridges to be perpetually in free fall. (ETA: This is actually true in a way, I'm an astro engineer.)

[@lidular]

So knowing that grey obsesses over every single word used, I watched the video back. He never says that hexagons are the strongest shape. He says a hexagon tiling is very strong due to the 120 degree joints which is the most mechanically stable joint.

[@XatxiFly]

This. Can't believe what a huge strawman the premise of this video is when I was hoping it would add some interesting context.

[@googlepleasedonttakemyaccountf]

In most cases, two beams crossing will be stornger than three ends coming together. Depends on the material used and the way you join them ofcourse.

[@TheRealAlmostHooman]

I was under the impression that "strength" usually refers to how much force an object can take before breaking, not deforming. by that definition, strength and rigidity would be 2 separate things, but they're used synonymously in this video. is "strength" actually a clearly defined term across science and engineering, or can it refer to multiple things?

[@ConHathy]

With regards to materials you are right but I would argue that they are very much linked when looking at large structures. For example, the bridge at 8:00 didn’t fail in the material sense where a member broke from stress, but if an engineer tried to argue that the bridge was perfectly strong you probably would disagree because it collapsed under its own weight. Also in terms honeycomb, triangles would actually be stronger because they are supporting some of the load unlike hexagons which are too flexible to really support the skin under tension or compression.

[@NWinnVR]

I just think they are pretty...

[@Sapioso]

Salma Hayek of shapes 😍

[@mitchjohnson4714]

Me too, but I think octagons are prettier. They don’t tesselate, but if I can add some squares, that’s a beautiful pattern.

[@CyrusOfNaias]

I prefer Octagons

[@krissyai]

I think he's, pretty..

[@Joneender]

@@CyrusOfNaias octagons can only tile with squares included, and are basically squares with the corners cut off :/ i wont judge what shape you like tho

[@ymiros0953]

While I understand what you are trying to say at 5:00, molecules do most of the time really like specific angles and are a bit more like stiff joints, so even without any repelling/attracting forces of atoms not directly bound to one another the hexagon wouldn't just collapse into a rectangle

[@kundudev1449]

this answers my question when I saw the smartereveryday ULA tour vid where that (presumably interstage) part was milled in triangular grid and not hexagonal as CGPgrey said hexagons are the bestagons. I believe the physics of packing materials most efficiently (where hexagons are the bestagons) and the physics of static determinance (where triangles are best) is quite different but visually the same and leads to incorrect correlations.

[@chaos.corner]

Efficient packing is still triangles. It's just that *neighbors* are in a hexagon.

[@TheRealE.B.]

@@chaos.corner 2D efficient packing, right? Because in 3D, I think you need a mixture of hexagons and pentagons. Like a soccer ball. Your body is made up of cells, many of which have hexagonal and pentagonal sides.

[@chaos.corner]

@@TheRealE.B. I'm not familiar with cells (which aren't spheres and rave their own raison d'etres for how they are) but for spheres, hexagonal close packing has two different configurations. The smallest arrangement between any four touching spheres is a tetrahedron.

[@TheRealE.B.]

@@chaos.corner Hmm. Maybe it matters if space is the only concern, or if you have to worry about physics like pressure, surface tension, boundary conditions, etc. I don't know. I admit that this exhausts my knowledge on the subject.

[@chaos.corner]

@@TheRealE.B. Yes, it's entirely about the space left over by sphere-type objects.(atoms are a bit different as it's about minimizing the energy of the bonds). Boundary conditions can definitely affect things too. Consider that cube-type cells are going to stack in a fairly linear fashion.

[@BirnieMac1]

The hexagonal sheets too often form aromaticity - which causes the electron clouds to delocalise to WITHIN the hexagonal carbon rings. I.e. the repulsion you described but your supports aren’t limited to the nodes This causes them to have a very different property to a normal hexagon like you discussed and may be why there’s that observed disconnect for why hexagonal organic structures Your simulation at around 6:20 shows this well; because its going to behave more like cyclohexane instead of graphene It’s remarkable how well the addition of the triangles simulates that aromaticity There’s a reason we often denote aromaticity in organic chemistry with a circle though; because in reality the electron clouds behave like one. In otherwords if you increase your no. triangles from 6 to infinity; the resultant circle inside the hexagons with triangular braces is how graphene and aromatic lattices behave You’re super close with your simulations, but if you check the electron density diagrams of graphene,you’ll see what I mean

[@KatieDawson3636]

Chemistry background. They definitely aren't strong in the traditional structural engineering means. Hexagons are really great because of their ability to balance strength with space-filling efficiency - which is really the reason behind the honeycomb tiling and of course, actual honeycomb. Getting rid of that "extra bit" you talked about can be okay in certain situations (like where there will be a backing, like a wall, panel, or floor) but you want walls or compartments. Basically, when there is a single dropplet, a circle is favored because it maximizes volume/area and minimizes surface/perimeter. If you have many dropplets together, hexagons are the shape that provide this ideal ratio. Generally, I wouldn't call them "strong" so much as "efficient." I would like to note of course in chemistry the resonance structures in benzene as well as to some extent the stability of cyclohexane (although technically it isnt a 2D hexagon). These molecules, and benzene in particular, show immense stability, which we colloquially refer to as the "strength" of the bonds. But also, hexagons might not resist compression well, but they do resist expansion (like if you blow up a balloon inside). I think these ideas are where this "strength" idea comes from.

[@CielMC]

I'm loving the science and physics, I'm glad I was recommended this video, keep up the good work

[@Darth_Insidious]

The main thing going for hexagons is that they are the highest sided shape which can form a regular tiling. The more sides a regular shape has, the lower the ratio is between perimeter and area. Circles have the lowest ratio, but can't be tiled and always leave some space in between them. So hexagons are the shape to subdivide the greatest area with the least amount of material. Triangles are strongagons, Hexagons are efficientagons.

[@anthonypacillas4830]

And what are squares?

[@Darth_Insidious]

@anthonypacillas4830 Squares are easy to cut and can be turned into the strongest shape, triangles, with a single reinforcement between the corners. Squares do use more perimeter than hexagons to enclose the same amount of area, however.

[@anthonypacillas4830]

@@Darth_Insidious Hmm, I will need to soul search more info.

[@mrwoodandmrtin]

Tell it to the bees. Well the beehives. Agree. Triangles for strength, but hexagons for filling area uniformly. Storage option in other words. Basically, a bunch of tightly packed circles (Minimum perimeter for volume optimization) but without all the unused space between the circular cells.

[@Mike-mf3ed]

I was taught in school that polygons are shapes with “more than 4 sides” which also excludes Triangles. I’ve gone by that logic for years and now my reality is shattered. But even if Hexagons aren’t the Bestagons, they’re still my “Favourite-agons”.

[@chaos.corner]

Your simulations remind me a bit of "world of goo". You get to build structures out of members with various properties. Triangles are the rule of the day. At least in critical points. I may have to dig it out again now.

[@Greenicegod]

That was such a great game! I'll have to search for it again

[@walugusgrudenburg3068]

I'm still incredulous that the game's getting a sequel!

[@this-one]

I was gonna comment the same thing, especially when I saw that triangle bridge simulation!

[@chaos.corner]

@@walugusgrudenburg3068I'm incredulous the game is $15 after all this time. I have a copy somewhere but can't find it.

[@SokarenT4S]

funny how theres gonna be world of goo 2 now

[@LegalizeAlejandro]

Im not so sure if hexagons are really the bestagons, but I’m 100% certain that the cinnamon is the winna mon

[@JoeBrowning-n9k]

Oh boy. 🙄

[@Averagequinoafan]

*CGP Grey wants to know your location.*

[@telotawa]

the reason graphene's hexagons are strong is kinda several factors, but you did good enough there's also VSEPR, for example, which is basically lone pairs and molecular bonds repel each other, which is why water forms a bent shape! so, benzene forming a flat hexagon is a result of that and what you said and maybe a few other things. it pushes itself into that shape, and that sure as heck doesn't happen if you just make any random hexagon on the macro level

[@noeschaeffer2167]

Can you develop your point about VSEPR? How does its principle that lone pairs repel molecular bonds more than molecular bonds repel each other factor into graphene’s hexagons being strong?

[@b3n9y74]

Obviously triangles are stronger than hexagons, but the reason honeycombs are comprised of hexagons is because they offer an optimal compromise between structural integrity and material usage. The simulation at 6:00 -- while very cool -- is somewhat of a moot point since (as u later explain) it is "wet spaghetti". Circles and triangles are the strongest 2D shapes but interestingly both form hexagonal patterns when packed together

[@sagielevy]

Hexagons are not only a shape. They are the light, the are the truth. They are a way of life. In Hexagons we trust. Save your hexablasphemies good sire

[@mangelsimonpaniello2256]

I just discovered this channel, and I gotta say, the 14 second intro already made me subscribe

[@GameyRaccoon]

things heating up in the geometry fandom

[@_questionmark_]

I used to be on team hexagon, I agreed completely with Grey's analysis when I first saw it. But, I have since matured and now my one and only true shape love is the circle, perfectly even all around, symmetrical, pure and able to smoothly roll on a flat surface. You need only look around you to find that circles are everywhere, with endless uses. Praise the circle. o

[@NicosKaralis]

My whole life is a lie, what's next? The mitochondria **isn't** the powerhouse of the cell?

[@LucyTheBox]

How could you? I was indoctrinated into the bestagon cult three years ago, and have been a faithful believer all this time! How dare you shatter my faith like this?!

[@potionmanblues]

DO NOT LISTEN TO THIS SLANDER, HEXAGONS ARE STILL THE BESTAGONS

[@darekarashish]

Quick, somebody quickly tell all honeybees that they've been building all honeycombs wrong all this time!

[@oliverdowning1543]

Honeycomb is also the best shape in terms of both tiling and having a large area to perimeter ratio (which is why bees use it in actual honeycomb). But that's not a strength thing that's a material efficiency thing.

[@SirPhysics]

Bees don't actually "use" hexagons. Bees make cylindrical cells in the wax, which become hexagonal due to wax being able to flow when warmed up.

[@oliverdowning1543]

@@SirPhysics it still ends up that way and for the same reasons but that's super interesting thanks for sharing.

[@theapexsurvivor9538]

​@@SirPhysicsyep, and specifically it only forms the N-gon whose tiling best matches the packing used by the bees. If they used square packing instead, the forces acting on the comb would produce roughly square honeycombs. It also means if the packing is uneven, the comb will simply adapt to whatever polygon is best.

[@NihongoWakannai]

@@SirPhysics They do use hexagons. Why would they expend extra energy to "intentionally" create hexagons when the wax will naturally form that way? If another shape was better, they would be using that shape instead. The fact that bees honeycomb ends up as hexagons is BECAUSE hexagons are the best polygon for efficiently tiling a plane.

[@jpogigtxcr1778]

Being efficient is not the strongest.

[@artesiapiano4628]

As a beekeeper, Hexagons ARE bestagons.

[@UmbraResistis]

I think the biggest problem with the simulation is that the joints are free to move, which is not exactly realistic to life. In real life there is no joints which can just phase through each-other.

[@lucasklaassen135]

Unfortunately that's not how physics work. Joints, whether they're free to move or fixed, will always be the weakest point in a system if they can't simply pass the force straight to the next side. Remember when Con said materials are strong if you push or pull on them, but not when you bend them? It's basically that.

[@justv7536]

You can fit 6 triangles in a hexagon, that makes it 60x the strength and 6000x the cool factor

[@wunderkindt]

came here for 3d printing, stayed for the knowledge. !תודה רבה

[@allstarwoo4]

Im sorry but im with the hexagons are the bestagon for that one reason, manufacturing. You're right with rockets where weight is everything being able to cut a few grams is worth it. The thing is most manufacturing doesnt need that level of weight savings. In fact i think that me being to go and just buy honeycomb structure is incredibly useful for any project id want to do. You technically could make your own custom trigular structure but then the question becomes is the time you put into making that structure worth the weight savings? And most cases, no. I came from working on cars so my idea of engineering is much more pragmatic than a true engineer.

[@SheaValentine]

Hexagons are useful additionally for these reasons: - They have good packing properties - They are good at retaining their shape after elastic compression - They are good at resisting internal pressure. Basically, they're circles.

[@matthewparker9276]

That's the real benefit of hexagons. They're the best approximation of a circle that monotiles the plane.

[@blacklight683]

Wait didnt he say they are the best because they can contain the most while using the least amount of materials(borders)while being stackable

[@hectorvillagran177]

Tension is strong, compression is generally stronger. Buckling failures are in a way a type of tension failure where the material fails away from the neutral axis, usually on the side that it is in tension.

[@xandrewvondiue522]

I didn't watch CGP's hexagon vid, but am nonetheless glad that I found this corner of the internet where people nerd out about materials engineering & physics

[@garywheeler7039]

It all comes down to hexagons as volumes versus hexagons as a system of struts. Different things.

[@okarthegreat]

This is a really cool video. I'm not a professional when it comes to any kind of science, but when I saw that video, I never felt like it made intuitive sense that a hexagon would be stronger than a triangle. I really enjoy your way of explaining things, and I'm very excited to see more of your videos. Subscribed. :3

[@XatxiFly]

For the record this video is misrepresenting CGP Grey, who never said "the strongest shape," whatever that even means.

[@hypgnotic]

hexagons made of triangles are the bestagons.

[@rich_2739]

I'd be really interested to see a video discussing what -agon is the bestagon, given the constraint of the -agons starting from pentagons and rising in number of sides!

[@aspiringwayfarer]

Ok, but the claim that ‘hexagons are the best “-agons” ‘ is still true. Name a better “-agon”. I’ll wait.

[@OakPotatoo]

trigon

[@aspiringwayfarer]

@@OakPotatoo that’s an “-igon”. Sorry but still not an “-agon”.

[@OakPotatoo]

@@aspiringwayfarer trigagon

[@theOKguy]

fire breathing dragon

[@meapyboy12345]

@@theOKguy🤣😆😂you win my guy.

[@Fracsus]

there is 1 CGP Gray outside your door wanting to commit a crime

[@marcopohl4875]

On honeycomb panels: why don't we use a triangular spacer instead?

[@HelloKittyFanMan]

Cool video. Happy Christmas!

[@HappyHitman]

I love Greys video but i also love that this respectfully counters it. Scientific debate for the win.

[@stephenspackman5573]

Hexagons form triangular tessellations. I can believe that triangles are the bestangles, but hexagons are still the bestagons.

[@saeedgnu]

Hexagon is best for optimizing wall length compared to area when tiling. That's all. Every problem might need a different optimization.

[@keenansutherland2776]

homie you make an amazing point that I agree with. also, i may copy your facial hair...tbd. good video and communication skills

[@PvPsFinests]

The point of hexagon making a great spacer material between two strong sheets made me think of cardboard. Would a hexagon lattice between two fiberboards be stronger per material used that the corrugations?

[@benoitcerrina]

Yes and it is sometimes done but more complex and expensive

[@theapexsurvivor9538]

Yep, it doesn't have long lines where it buckles easily, making it much stiffer and harder to compress. Not really great for making boxes though.

[@ProtusMose]

This feels like finding out that Santa isn't real. I'm not sure what to do with my life now.

[@dadbear5316]

Triangles are the SECOND strongest shape, the strongest shape is actually a circle but circles are really hard to make so we've just made things out of triangles because they are much easier to produce.

[@theapexsurvivor9538]

It doesn't help that the strength of a circle is way more dependant on its precision than any other shape, and given that a perfect shape can't exist outside of theoretical modelling, a circle will always have some point of failure in practice.

[@SM-ok3sz]

A circle is only strong when the force is equally distributed around the circle and is orthogonal to its edge. Any other load configuration will cause it to buckle. That’s why arches only work when loaded at their apex with the force parallel with gravity. This is also why gas tanks are cylinders because gasses expand to fill a volume and exert equal force on its surface.

[@hypertectonics7009]

Am I wrong in pointing out that your simulation shows all joints freely rotating, while in reality hexagonal grids are all rigid joints, and you just somehow glossed over this situation saying that "overconstraining a system introduces more stress". Isn't that what's actually worth explaining, how the stress distribution of a rigid hexagonal grid fares compared to other kinds of rigid grid structures, and the facts you mentioned about statically indetermined grids of flexibly joined hexs are just... a red herring?

[@Tehn00bA]

"Sir, this is still a Wendy's."

[@inkuii]

As a chemist: hexagons are still the bestagons Triangles are evil.

[@Jacob-yg7lz]

The main real advantage of hexagons is that they approximate a circle and thus are the tileable polygon that requires the least perimeter for an area, which is why they're good for honeycomb paneling

[@Pinoccappuccino]

I haven't seen CGP Grey's hexagon video or any of his video for that matter (unless he has a video on flag colors, I may have seen that), so the KZbin algorithm suggested this video more out of nowhere. You still have my interest though.

[@Leadvest]

This really highlights how important context can be.

[@MohamedAshraf-vq1vu]

11:42 "I know it's no square-agons it's 4 the bit" Best unintended pun ever

[@hkayakh]

7:15 to be fair, Grey was talking about hexagons in a flat plane and not a vertical plane

[@bryananderson688]

If the vertical plane collapses because gravity pulled down on it, what will the horizontal plane do when something pushes across it?

[@RocketSlime]

​@@bryananderson688pretty sure you can overlap layers and make the structural integrity amazing

[@Baaluluna]

7:31 the important thing here isn't that the triangles hide hexagons, but that the hexagons hide triangles

[@sideways5153]

One of the only commercial products I've ever personally handled in my life with a hexagonal pattern is chickenwire - a fine mesh fencing material used for low-strain applications. If hexagons are superior, consider: why are nets and chain link fences always made with a square pattern? Why are fabrics made with a square pattern in the textiles? Basically, if hexagons were the best shape for everything, we'd bother using them more often. Most of the time, they're more effort than they're worth - but sometimes they do get used, because there are times when hexagons are the best solution!

[@Zopoko]

Regarding fabrics, they are not always made in a square pattern. Most fabrics used to be square because of the ease of manufacturing them (weaving), but there's also non-square fabrics like Jersey, which is knitted. If you take an old T-Shirt or a knitted scarf, give it a good stretch and look at the holes, you'll see that they'll actually form some kind of hexagonal lattice. Which perfectly aligns with the point of the video. Hexagonal (knitted) fabric = Stretchy in all directions Square (woven) fabric = Rigid along the X and Y axis, but stretchy if you apply diagonal tension (this turns the squares into rhombi)

[@MorgenPeschke]

Nets are generally made in a diamond pattern, not a square pattern. Yeah, it seems pedantic, but it's significantly easier to keep everything consistent if you're tying them in a diagonal lattice because each knot is in the middle of two other knots, so you can control the height of the diamond by using the width of the netting needle (they're much wider than the name suggests) and once the first row is established it's comparatively easy to place each knot between two knots in the previous row (tension and gravity do much of the work). The reason they're not hexagons or triangles is primarily because each knot weakens the load capacity of the line, so minimizing the number of knots is a very desirable property and diamonds are a good balance between ease of manufacture and minimization of the number of knots.

[@bugjams]

Easier to make that way + cheaper + people who make fabrics/nets/fences are not mathematicians or physicists.

[@davidegaruti2582]

It's faster to replace damaged fabric rather than making super strong hexagonal fabric

[@MichailAgustusSolomonic]

I wondering "why all house build square/tetragon if hexagon is bestagon?". Well a cube has only 6 sides to finish, meanwhile hexagon must has 8. Also why liquid/water tank all in cylinders? because bees actually build its hive on concept of cylindrical containers. But because wax easily to merged so each triangles left became 120° junction.

[@chrimony]

Out of curiosity, what software are you using for your physics simulations?

[@ConHathy]

This was just something I threw together in Matlab and eventually it turned into this video. Definitely not the fastest way to do it but it works

[@kundudev1449]

@@ConHathy Figured it was matlab, but I would like to see how you simlated the physics. If you could somehow make the code public for us to try... I would really like to learn from it.. Thanks in advance

[@shaider1982]

Nice thing about hexagonal holes is that the material around each is of a single width unlike an array of holes. Plus, the holes cover the fan efficiently

[@anon_y_mousse]

The real reason hexagons are the bestagon is because they look cool and are great for RPG terrain.

[@theoriginaledi]

I have no argument with your engineering, but I still contend that hexagons are and shall always be the coolestagons. Triangles are great too but they just don't have the edginess and panache of a hexagon.

[@Helperbot-2000]

always hilarious that when the hexagons are left to themselves they try to turn into rectangles, shapes grey seems to dislike :P

[@Best_Blake]

The video was about how they're the best for tiling not the best individually. In that case CGP grey is right you he said that in the video the triangle is the best individually but when tiled hexagons are the best.

[@lemonadonGD]

Hexagons aren't the strongagons, but they probably still the bestagons

[@lambda7285]

I literally came from a video 4 years ago saying "Hagons is the bestagon" and see this video in my recommendations

[@lambda7285]

Yk when you don't take time to listen before saying some shit

[@TheBluePhoenix008]

I would sure love to tell Grey about this, if only there was a method to comment on his videos

[@AzureAlliance31]

We need video responses back

[@TheBluePhoenix008]

​@@AzureAlliance31 knowing him he'd ban those too

[@wesbrown2105]

i have an issue with your sims. in the case of a hexagon and its strength, wouldn't it matter if it is filled with a fluid. a can of soda is very weak until it is filled with fluid to add structure.

[@IsYitzach]

The one that bothered me was that Grey said that bees make it because reason that I forget. Turns out, as Matt Parker found out, they make as a side product of how they make shapes.

[@Alex-d3l9b]

Packing efficiency, circles leave space unused.

[@That_One_Kobold]

No shit, they have evolved that way specifically for the packing efficiency

[@gokalpcetin4763]

I feel like there are some points missed, it's almost like this video is made before carefully listening to CGP grey's video but still referring to it. Congrats you created a paradoxagon!😅

[@ConHathy]

He did make good points, I’m only addressing this one small part of his video

[@That_One_Kobold]

​@@ConHathydude he never claimed that Hexagons are the strongest, he said they're strong, not strongest.

[@ConHathy]

@@That_One_Kobold strong relative to what? Of the regular polygons, only triangles quadrilaterals and hexagons can tile. Triangles are the strongest, quadrilaterals are optimized for forces in two directions (see ULA), and hexagons are wet noodles by comparison. What are they stronger than exactly?

[@Blotz0]

Hexagons are the bestagons for math, but not for physics.

[@detoxeg1664]

well, your experimental setup is a bit off because you are more testing how well something holds its own shape without having fixed corners instead of providing structural integrity of the whole thing