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A sunflower at infinityThis picture by +Roice Nelson shows the ‘view at infinity’ of a honeycomb in hyperbolic space.

A

honeycombis a way of chopping space into polyhedra. For example, we can chop ordinary 3d space into cubes. This is called the{4,3,4} honeycomb. Why?• a square has 4 sides so its symbol is {4}

• a cube has 3 squares meeting at each corner so its symbol is {4,3}

• the cubical honeycomb has 4 cubes meeting at each edge so its symbol is {4,3,4}

The picture here is a view of the

{3,3,7} honeycomb. This is defined in the same sort of way, but it doesn’t fit into ordinary Euclidean space. It fits into a curved space calledhyperbolic space!The honeycomb extends forever, and it forms this pattern where it meets the ‘plane at infinity’ of hyperbolic space.For links to related pictures, visit my +American Mathematical Society blog

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