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  "body": "\n## Summary\n\nA sphere packing is an arrangement of balls in space that do not overlap.\nThe classical question asks for the largest fraction of space that a packing of equal balls can fill, its [[packing density|4P5PSWADJD]].\nThe answer is known in dimensions $1$, $2$, $3$, $8$ and $24$.\nIn the plane it is the hexagonal packing, and in space the face-centred cubic packing of the [[Kepler conjecture|AFMBQT06ZV]].\nIn dimensions $8$ and $24$ it is given by the [[E8 lattice|2CXH65EKY7]] and the [[Leech lattice|XETV3657DG]].\nSphere packings are linked with error-correcting codes, lattices, number theory and crystallography.\n\n## Explanations\n\n### L1 human\n\nThink of oranges stacked in a crate.\nA sphere packing is any way of placing equal balls so that none of them overlap; they may touch.\nStacking layers of oranges so that each orange sits in a hollow of the layer below fills about $74\\%$ of space.\nThe same question makes sense in the plane with coins, and in higher dimensions with balls that cannot be drawn but can be described by coordinates.\n",
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