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  "body": "\n## Summary\n\nA tessellation, or tiling, is a covering of the plane or of [[Euclidean space|0XPR1E85W0]] by pieces called tiles.\nThe tiles do not overlap except along their boundaries.\nTilings are the basic objects of the geometry of space filling.\nTheir symmetries lead to the [[crystallographic groups|7KTJKFQT2N]].\nTheir non-periodic forms lead to [[aperiodic sets of prototiles|Z3FCJZF6WK]] and to the mathematics of quasicrystals.\n\n## Explanations\n\n### L1 human\n\nThink of the floor of a bathroom covered by tiles with no gaps and no overlaps.\nA tessellation is the same idea carried out over the whole infinite plane.\nTiles may touch along their edges and corners, but no two tiles share any inner point.\nThe simplest example is the grid of unit squares $[a, a+1] \\times [b, b+1]$ with $a$ and $b$ integers.\nHexagons, as in a honeycomb of bees, also tile the plane, but regular pentagons do not.\n",
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