this post was submitted on 09 Jul 2025
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Insufficiently hexagonal
You're on the wrong website pardner
I'm not saying this to be an argumentative debate-bro, and it's been a long time since I've forgotten abstract algebra, let alone found myself able to quickly work these things out, but l think usually where there are equilateral triangles, there are hexagonal symmetries (in 2d and 3d spaces)
I'll grant you that there's a square there, but there are no hexagons on that thing, I guess you could use 6 to make their bases make a hexagon tho :U
It's too late. I've already sloppily depicted my argument illustrating the flattening homomorphism between the tetrahedra and a hexagonal graph in multiple colors, without regard for anybody's eyes
What hexagonal symmetries mean is slightly different from a shape being made out of hexagons. If you were to take a hexagon and rotate it a certain amount or flip it you will end up back where you started. You can make a set of actions that keep the shape the same, that would look something like {60° rotation, 120° rotation, 180° rotation...}. That set is its symmetry group. If an object has hexagonal symmetries, it has the same set, so even if it looks nothing like a hexagon you would be able to do all the same things you'd do to a hexagon and keep it the same.
edit: source if you wanna learn more
happy cake day btw
thank you!