Hexagons Are NotSoGreatAgons

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.

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

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

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.

a hexagon is just 4 triangles

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

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

Triangles and engineers. The best love story.

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. 😩

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

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.

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

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

I just think they are pretty...

Things are heating up in the shape fandom

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

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.

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.

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

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!