As Twilight sparkle and her friends sat in front of the futuristic hexagonal holographic board at the back of the virtual classroom, sitting in their grey and white hexagonal seats, Grey simply spoke a single phrase to them.
"The first thing you need to know, is hexagon's, are the bestagons."
Simply saying the phrase made Grey feel like he was making progress, feel like he was truly getting somewhere. Though, he had barely even begun, and when the first question was asked, he was ready to pounce.
"But, why? It's so boring and it doesn't even make sense!" Twilight shouted angrily, feeling like she was being insulted for her beliefs.
"Why, you ask? Because, bees." Grey says as he pulls a bee hive out of thin air, as hundreds of bee's swarm around it, as Grey pulls out a piece of honeycomb from the hive. "Bees are the best, and build only the bestagon, the hexagon."
Fluttershy proceeded to raise her hoof into the air, as Grey pointed to her. "Yes, Fluttershy?"
"I heard they did it because they were hexapods that had hexagon eyes, so how could they do otherwise?"
"I am very glad you asked that Fluttershy, as it is a very good and valid point." The holographic board then displays an image of a bee. "The humble bumble has an engineering problem to solve. She makes two things, honey and wax." He says as images of a drop of honey, and a tub of wax appear on the screen. "The former to eat, and the latter to contain the former. To make but a little honey, she must visit a lot of flowers, and to make one unit of wax, she needs eight units of honey. Wax is costly for bees in flower terms, and honey is drippy in food terms. So to make a hive that contains the maximum honey and uses the minimum wax is royally vital." Grey says as the image of two bees holding up a paper, one holding and playing a bugle as the paper reads 'By Royal Decree: Reduce Wastage'.
"Thus, a honeycomb conjecture. Which shape, works best? To answer, we need to talk tiles." Grey says as he pulls out a holographic box and dumps it out, as a bunch of random shapes appear on the floor, as he gestures for his students to come closer, as they all get up from their seats and sit down on the floor with him as he crouches down. "Tiling is covering a surface with a pattern of polygons. There's lots of options, because there's lots of polygons. Even the regulars go on and on-agon. Now for bees, picking patterns..." Several images of complicated and advanced holographic patterns appear on the floor, as the ponies and Spike watch with amazement and curiosity. "The more complicated ones obviously use more lines than necessary, that's what complicated means. And thus a honeycomb of that tile would use more wax per honey. So sticking to the simple regulars, there are just three that tile tightly, triangle, square, and hexagon."
Suddenly, three tile patterns appear on the floor, with green triangles, red squares, and blue hexagons. Other patterns also appear. "Pentagon's are broken hexagon's, leaving gaps, same with septagons. Octagons are alright, but there no hexagon. This leaves the tiling trio that tile differently. A square is a square of squares, which is a square of squares, and so." Grey says as a red square hologram begins to infinitely tile, with Twilight and her friends looking on in confusion and amazement at this strange tiling process. "Squares tile tidily by basically cheating, covering an infinite plane with an infinite number of parallel lines."
"Hey, these squares are being unfair!" Pinkie shouted, protesting against the cheating behavior of the square.
"Indeed, Pinkie. Like, wow, that's what a plane is. Boring!" Grey says throwing away a square hologram he was holding. "Triangles pull the same trick, dividing themselves down into infinite nothing. But not the hexagon! The only regular polygon to tile a plane without resorting to debasing self division, unlike some squares I could mention... At least triangle is trying to be more geometrically interesting than the square, teaming up to... one, two, three, four, five, six... Wait, hexagon!" The ponies all gasped at this sudden realization, Twilight just being purely dumbfounded.
"The other shapes can't help it, they just want to be the bestagon. Even some of the irregulars like rhombus tile by hexagoning. Same with your triakis tiles, and deltoidal tri-trihexagonals, and your, ah, kisrhombiles, and floret-chuckle floret penta-pentanogals... Look, there all just hexagons." Grey lightly chuckled, continuing to struggle with saying the name of these shapes, Pinkie lightly giggiling at such weird shape names, while Twilight was busy taking notes, having never heard any of these shapes before. Meanwhile, Rainbow was busy snoring in her sleep, before Applejack lightly jabbed her in the side and woke her up.
"Hey!"
"Pay attention!"
"But it's so boring!" Grey just scoffed at Rainbow's lack of enthusiasm as he continued.
"Anyways, even cairo tiles, poor pentagons, tile up as best they can to form a lumpy hexagon. The rest, just can't compete, with the best. The hexagon, nobily indivisible, is the bestagon." Everyone slowly nodded, Twilight still being highly skeptical, but Spike and Pinkie nodding more rapidly, highly interested in this subject.
"Now where were we?"
"I believe we were talking about bees, darling." Rarity happily reminded Grey, as he pointed to Rarity.
"Thank you, Rarity, yes, we were talking about... Oh right, honeycomb conjecture. Max honey, min wax, three options." Suddenly, Applejack pulled out a large circle.
"And what about this then?" Grey sighed in annoyance, before understanding she had a valid point.
"Ok yes, there's the circle, a shape defined by the least perimeter for the most area, but that only works when you just need one." Applejack appeared confused, as Grey displayed an image of a circular honeycomb conjecture on the board. "Pack circles and this is the best that they can do, look at all that wasted space! And even if you pack the gaps, you still use more wax. And, again, the way these circles, arrange themselves... It's almost like... onetwothreefourfivesix Hidden hexagon!" Applejack was just dumbfounded by this revelation, simply sitting down and shutting up as she listened, understanding how the circle was not an option.
"Bees use the hexagon because no shape is better to create the maximum area, for the minimum wall. And this min-max stat of hexagon is one of the many reasons they show up everywhere, including in the aforementioned bees eyes." Grey says as a close up image of the eye of a bee is displayed on the board, with Fluttershy appearing slightly frightened, but also intrigued.
"Each hexagon is a long tube that leads to the light catching cells at the bottom. More light equals better vision and hexagon's let the most light in using the least amount of wall." Grey says looking at a the board, which had a video feed of Grey and the ponies through the eyes of a bee, with the girls and Spike being amazed at this information, with Twilight taking notes like a mad mare, but then asking a question of her own, hoping to disprove Grey.
"So why aren't our eyes hexagons?" Cue Grey using some good ol french, or in pony language, prench, against Twilight, as a beret spawned on her head.
"Au contraire mon ami, they are l'hexagon. Not on the outside..." Grey slowly got closer to Twilight's face, staring right into her eyes and speaking in a deep tone, which she found both terrifying and somewhat calming. "But on the inside. Your light catching cells are at the back of your eye in a hexagonal grid for the same reason as bees. Max light, min wall." Grey slowly backed away, before a hologram of a hexagonal window to outside the castle of friendship appeared, as everyone looked to it. "Your window to the world is but through the hexagon. Does that not make it the bestagon?"
To say Twilight and her friends were flabbergasted would be an understatement. In terms of agreement, Spike, Pinkie and Fluttershy were instantly on board with the idea of the bestagon, understanding its important. Applejack, Rarity, and Rainbow Dash were still a little skeptical, but Twilight was in full on denial.
"I still do not believe it holds any importance, it is simply a coincidence that it is part of us!" Grey got an angry look, as the holographic tablet he was holding to display the min-max of the hexagon was tossed away.
"Okay, maybe hexagon as min-max-agon doesn't catch your fancy. Then how about a little mystery, oui? Let us travel, to saturn, a planet from my universe within my galaxy, the milky way." The hexagonal window's view slowly started to shift, until a large planet with a massive ring around it was in view, as everyone's jaws hit the floor, Twilight's included. Twilight had never seen such a fascinating planet in all her years of star gazing. "Now yes, the rings are attention grabbing, but leave the equator, travel north, and here lies the un-explained..." The view of the planet slowly shifted, to reveal a giant hexagon shape on the north pole of the planet, with the ponies having their brains fried. "The Great Hexagon of Saturn. Need something for scale? Well, here's the earth, my homeworld." Grey says as an image of his homeworld appears next to the hexagon, with Twilight dumbfounded by the scale, and about to question it, before Grey continued, as five more earth's appeared around the hexagon. "Oh, here's six the Earth's. Saturn's hexagon is, pretty big."
Suddenly, the ponies and Spike all appeared in advanced space suits alongside Grey, who was opening the hatch of a space station. "What is it, you may ask? Well, you might be thinking its a geological formation..." Grey says as they appear on solid ground next to a massive hexagon pillar of stone. "A massive basalt column, like the smaller versions you find on Earth." Grey says as a holographic screen displays the image of a stick person climbing on said pillars. "But no, Saturn is a gas giant." Suddenly, the ground beneath them disappeared, as everyone began floating in zero gravity, the rock included. "There is no surface or geology to speak of." The basalt column promptly vanished when he said geology.
"So, the great hexagon is composed of shapeless clouds, somehow keeping shape, and changing color." Grey says as everyone looks up in awe to see a massive swirling mass of clouds, changing color from light blue to orange, until they suddenly appeared in space, hovering above the planet in space, as Grey donned a special hat. "It's a magnificent solar system mystery. And, while I am no space archaeologist, if I was looking for an alien gifted monolith on the most 'Look at me' type planet, under a hexagon beacon with earth-sized sides, that's where I would start." Grey said clicking his tongue. "After all, what aliens would want to make first contact with the nearby monkeys before they became enlightened to pursue the universal truth. Hexagon, is the bestagon." Grey says as everyone re-appears back in the classroom and in their seats, still amazed by what they saw.
"Wow... Hexagon's are cooler than I thought!" Spike shouted with enthusiasm, as Grey chuckled.
"Indeed, and in some cases, they are literally cool. Say, for example, this tiny snowflake I happen to have, that has six sides as all snowflakes do." Grey says as a snowflake materializes in his palm. "Gee, what could cause that to be? Let's zoom down to the atomic level and see." Suddenly, an intense zoom effect was put on the snowflake, as a close up appeared on the holo board, displaying several water molecules. "When water molecules join together to make a flake, the sturdy shape they prefer is a hexagon." Grey says as millions of molecules can be seen slowly forming together into a massive pattern of hexagons. "As more molecules join, they extend the flake fractally up,the beauty of the snowflake on the monkey scale is but an extension of the hexagonal perfection, on the atomic scale." Suddenly, Rarity raised her hoof into the air.
"But what about snowflakes with twelves sides darling?" Rarity says as one such snowflake appears in her hoof.
"Ok yes, you will sometimes find snowflakes with twelve sides, but this happens when two growing snowflakes get stuck together, so it still counts." Seeing the flawless logic in it, Rarity nodded and tossed away the flake. "And the hexagon isn't just for snow, it's for all ice One-H, which means basically all ice on Earth, and in Equestria." Grey then walks over to a wall with some vials in little hexagonal holes as he pulls out a vial from within the hole marked as Ice One-C. "Yeah, there's a little ice One-C, but we don't talk about it because it's made of cubes and cubes are boring, and there is a bit of Ice-9." Pinkie made a sound of audible fascination as she slowly extended her hoof to touch the Ice-9, before being stopped by Grey. "No, don't touch that." Grey then points to a glass full of water with ice cubes in it. "But if there is ice in your drink, give thanks to the hexagon for keeping it cool. And it's not just water, lots of atoms use hexagons because..." Grey quickly turns to Twilight, who has a pencil and paper gripped with her magic. "Take a note, Twilight, hexagons are the bestagons!"
Twilight was starting to get fed up with this strange being constantly stating this fact over and over again, refusing to note down his phrase but still note down the facts he brings up.
"Oh, using a pencil? Get ready to have your mind blown about the hexagon here too. The lead! Well, it isn't lead lead, it's carbon. And you know what carbon atoms think is the bestagon?" Cue an audible finger snap, as Grey produced two fingers to pull it off. "The hexagon! Pencil graphite is a whole bunch of hexagonal carbons, and when they happen to be in a straight sheet, that's Graphene, which happens to be the strongest atomic material in the universe, some of which, is in that pencil." Grey says pointing to the pencil in Twilight's grip, as she had a look of pure amazement on her face. But she quickly deadpanned before anyone could notice.
"Oh, and where's your proof?" Suddenly, two machines appeared between her and Grey, as they slowly began pulling on two sheets, one of graphene and one of steel, the steel being easily stretched with a number reading zero point four gigapascals, while the graphene hardly moved as the machine rapidly shook, reading at one hundred and thirty gigapascals.
"Well, Twilight, to tear a sheet of graphene apart, you would need a hundred times more force than to do so with steel." Grey said as the steel was ripped apart, while the graphene held firm. "Hexagon, is strong-a-gon. This is because when hexagons come together, they form three-sided joints one hundred and twenty degrees apart. This, for the least material, is the most mechanically stable arrangement. Pull on one joint, and the other two equally pull back. Push in and the other two are most able and stable to resist. Now look anew at a tiling of hexagons and you see it is nothing but these max stable joints, each arranged perfectly to help the others be stronger and stabler. This is another reason hexagon's show up everywhere. The universe blesses stability in her physics, from those basalt columns, to bubbles which, as soon as they can, ditch their spheres to become as close to hexagonal perfection as they can." Grey said as he stared at the bubbles he had on a plate along with Pinkie and Spike. "That's so cool." Everyone continued to watch in amazement, before Grey looked back up to the ponies and got next to Twilight.
"Oh right, yes. So if your pencil lead contains some of the strongest material in the universe, how can you write with it? Okay, okay, this is going to get even more exciting. While hexagons are super strong this way..." Grey says as the board displays a green arrow pushing against a row of hexagons, resisting against the force. "They aren't super strong this way." Grey says as the point of view changes to the side, as a green arrow pushes down into the hexagon pattern, forcing them down. On a small scale, that means your pencil can break off in layers that leave a mark, but on a big scale, hexagon's can be flexible while keeping their strength, letting us construct some totally unreal materials." Grey says holding a cardboard cut out of a hexagonal grid, as he lightly bends it before folding it into a cylinder, and then gets on the ground as he starts cutting away at a new grid on the floor, with Pinkie and Spike helping him.
"Print out a grid of hexagons in whatever, from aluminum to cardboard, sandwich them together, and pow! You've got honeycomb paneling, a ridonkulously tear-resistant material that's also super light and flexible." Grey then sandwiched three grids together between two pieces of cardboard and produced said paneling, with everything watching in amazement, Twilight being flabbergasted with this knowledge, as her whole anti-hexagon world came crumbling down.
"It's used everywhere, but particularly in human aviation technology." Suddenly, a video of a rocket blasting off appeared on the screen, as everyone watched with curiosity. "Rockets need to be strong yet light. Same for aircraft, with wings that really can't tear, but also need to bend. And only the magic of the honeycomb panel can do both as well. Give thanks to the hexagon for blessing our flight- Well, technically not your flight, it's my races flight, but still." Rainbow dash was simply dumbfounded that the hexagon helped these humans achieve flight. Maybe she could race one of these planes...
"And we still haven't yet discussed the most important application of the hexagon. Games!" Grey said as images of different game boards appeared on multiple floating hexagon screens, while the main screen had the image of two cave men fighting. "For centuries there has been great debate over boards, squares of hexagons? Spoiler, hexagon's win. Square boards are the first thing an un-enlightened species would think of. They look sensible and are easy to implement, but they are terrible, ineffective boards that cause spatial suffering. On a square board, move horizontal or vertical one space, and you've moved one space, but move diagonal and the square root of two spaces. Gross." Grey said as his skin became green like he was ready to barf, with Pinkie and even Twilight emulating the feeling. "Diagonals warp the distance pieces move. Square boards look neat and tidy, but it's deceitful. Their diagonals corrupting the meaning of space and time, and of course they must, because a square only has four true neighbors. Hexagons, however, have six, which is more than four, which is better! The distance from each space is the same in every direction. One space. Just as it should be. If you're a game based on squares, I'm so sorry."
Grey says as he and Twilight looked at a square chess board. "But, there is hope. With thought and effort, you can hexagon yourself into a better place." Suddenly, the board transformed into the shape of a hexagon, which Twilight found oddly beautiful in design. "As we all should aspire to do, spreading order and hexagonal enlightenment. For, hexagons..."
And like clockwork, all of the ponies, and Spike spoke up collectively and happily. "Are the bestagons!" Suddenly, the room changed, as an altar surrounded by candles could be seen, with a golden glowing hexagon at its center, as Grey stood in front of it, wearing a hexagon necklace and a white robe.
Twilight slowly stepped forward, a look of sadness on her face. "I... am sorry I ever doubted the worthiness of the hexagon, Grey."
"That is fine, Twilight sparkle. In accepting the superiority of the hexagon, you, are enlightened." Grey said as he placed a necklace with a golden hexagon on it, around her neck, as well as her own white robe, doing the same to each of her friends. "You are all enlightened. Welcome, to the order of the hexagon. Now, go, share the enlightenment of the order with others. And if you ever need my assistance, just tap your necklace, and I shall come. Farewell."
And with a flash of light, Grey vanished, as the holographic classroom dissipated, proud of a job well done. Twilight and her friends were unsure of what to think of the situation, but one thing was certain to all of them.
Hexagons, are the bestagons.