Honey bees build complexes of hexagonal wax cells in their nests to contain their larvae and stores of honey. Why do these insects prefer hexagons to, for instance, square cells (which are more straightforward to build)?
There are two possible explanations. One is that hexagon tiles the plane with minimal surface area. This claim (for obvious reasons called the “honeycomb conjecture”) was proved only in 1999 by Thomas Hales, and implies the hexagonal structure uses the least material to create a lattice of cells within a given volume.
Another explanation is that the hexagonal shape simply results from the process of individual bees putting cells together, somewhat analogous to the boundary shapes created in a field of soap bubbles. In support of this theory, it is observed that queen cells, which are constructed singly, are irregular, with no apparent attempt at efficiency.
Graphene is a two-dimensional indefinitely extending sheet of covalently bonded carbon atoms, which form a structure similar to that of a tessellation of hexagons. Graphite, found in pencil leads, consists of innumerable layers of graphene stacked on top of each other.
Its isolation was deceptively simple; after many years of trying to grow single layers of graphene on a matrix, some researchers simply took some tape, sticked it on some graphite, and peeled the tape off. A single layer was produced!
Graphene is aromatic; each carbon has 3 bonds, and one single pi-electron from each atom is delocalised across the entire plane. Consequently, graphene conducts electricity across its plane; for this reason, graphite also does so in the direction parallel to the graphene sheets that constitute it.
This is why graphene is seen to have great promise in technology; it is both transparent and flexible, and can also conduct electricity. As a result, it has been proposed to be used in various applications, such as solar panels and touchscreens.
It also has exceptional tensile strength; compared to steel of equal thickness, it is 100-200 times stronger. This has led it to be considered as a structural material; tennis rackets and cars made from graphene have been produced.
Commissioned by Chinese construction company CCCC who are currently working on a bridge to connect Hong Kong, Macau and Zhuhai, this concept for a floating metropolis by AT Design Office is surprisingly plausible compared to similar projects. It has been designed utilising the same technologies being used in CCCC’s bridge design; itself having a large submerged section that must be constructed on land and moved into position.
Comprised of prefabricated hexagonal modules tessellated together to form an island, the concept would be connected via transportation networks of submarines and yachts, and would feature expansive green spaces above and below the waterline that would provide areas for growth and recreation. Underground tunnels would also provide roads and walkways between modules.
Chat Noir looked up from the chaise in Marinette’s bedroom to find her looking at him with piercingly blue eyes. He looked down at his hand, fingers tipped with claws, and skin covered in the fine black tessellating hexagons of his suit. He’d wondered about it himself, but Plagg had been uniquely uninformative about the limitations of his strengths, and weaknesses.
“No,” he said, after thinking about it. Marinette tilted her head at him, and he sat up, flexing his fingers, thoughtfully. “Things hurt,” he admitted, “but not as much as you’d think.” He’d been thrown off a building, and could bounce across the road without so much as a bruise, although they hadn’t exactly been comfortable. “The suit’s magic,” he said, softly, “it protects me from a lot.”
Marinette hummed, wordlessly, and turned back to her homework. He’d told her he’d sit patiently and wait for her to finish it, because he wouldn’t be responsible for her being grounded on account of poor grades. He’d planned to let her finish it, without interrupting her, but the question, and subsequent murmur, made that difficult.
“Worried about me, Princess?”
“Yes.” He hadn’t expected that answer, and he looked at her as if seeing her for the first time. She wasn’t looking at him, but he got the impression she was deliberately not looking at him, rather than concentrating hard on her studies.
“Don’t be,” he said, eventually.
“You’re too self sacrificing,” she replied, her voice suddenly quiet. “You take hits for Ladybug all the time. I just,” she trailed off, her head bowing slightly, “wondered if they hurt.”
Chat felt his throat tighten as he looked at Marinette. He tried to reply, but found his jaw worked uselessly until he grit his teeth, his shoulders slumping. “They don’t hurt,” he said, finally. Much.
Marinette nodded, the corner of her mouth twitching faintly in a sad smile. “At least there’s that.”