Mathematician Solves the Centuries-Old Sphere Problem in Higher Dimensions

It’s possible to build an analogue of the pyramidal orange stacking in every dimension, but as the dimensions get higher, the gaps between the high-dimensional oranges grow. By dimension eight, these gaps are large enough to hold new oranges, and in this dimension only, the added oranges lock tightly into place. The resulting eight-dimensional sphere packing, known as E8, has a much more uniform structure than its two-stage construction might suggest. “Part of the mystery here is this object turns out to be vastly more beautiful and symmetric than it sounds,” Cohn said. “There are tons of extra symmetries.”

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