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Hexagonal Tiling Honeycomb
This picture by Roice Nelson shows a remarkable structure: the hexagonal tiling honeycomb. What is it? Roughly speaking, a honeycomb is a way of filling 3d space with polyhedra. The most symmetrica…
The Eisenstein integers are closed under addition, subtraction and multiplication, and they form a lattice in the complex numbers: The basic idea was to assume there’s a point in that’s not a hexagon center, choose one as close as possible to the identity matrix, and then construct an even closer one, getting a contradiction. But I’m especially interested in interpreting the other features of these honeycombs — not just the hexagon and square centers — using ideas from algebraic geometry.
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