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Lattices in the sense of discrete subgroups of Euclidean spaces, as used in number theory, discrete geometry, Lie groups, etc. (Not to be confused with lattice theory or lattices as used in physics! For lattices (ordered sets), use the tag: [lattice-theory])
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Understanding sphere packing in higher dimensions
The image below depicts a hypersphere inscribed in a hypercube. The number of dimensions increases from left to right (2,3,4 and 5 dim).
As you can see, the higher the dimension, the higher is the num …