Hexagons Are NotSoGreatAgons

Today we're talking about whether hexagons are really the bestagons. I'm sure you've already seen CGP Grey's iconic video, and it is a great video, but he claims that hexagons are the strongest shape and that's just not true.

(0:00) - Intro
(1:07) - Strength of Materials
(1:57) - Theory 1: Graphene
(3:44) - Hexagons are Unstable
(8:06) - Theory 2: Honeycomb Panels
(13:24) - Bonus Simulations
(14:21) - Outro

[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.

[JustAlfy]

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

[Albtraum_TDDC]

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

[MilkyWayWasTaken]

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

[athertongraham]

Things are heating up in the shape fandom

[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.

[andrewkuebler]

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

[rkond]

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

[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.

[andrewpeachey]

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. 😩

[potionmanblues]

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

[dsmith]

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

[youkofoxy]

Triangles and engineers.
The best love story.

[VoltByte_m]

I hope cgp gray sees this

Even if the hexagon isn’t the bestagon it still looks good

[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.

[forgerulethemall]

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

[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.

[ottekitfun]

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.

[omgitscake]

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.

[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!