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  "body": "\n## Summary\n\nThe Schläfli symbol is a short notation $\\set{p, q, r, \\dots}$ for a [[regular polytope|F60PD912D5]].\nThe first entry gives the polygons that form the two-dimensional faces.\nEach further entry says how many of the previous pieces meet around a face of lower dimension.\nThe symbol determines the regular polytope up to similarity, and reversing it gives the dual polytope.\nIt is the main bookkeeping tool in the [[classification of regular polytopes|XYCD53PB5K]].\n\n## Explanations\n\n### L1 human\n\nThe symbol $\\set{4, 3}$ means: faces are squares, and three of them meet at each corner; this is the cube.\nThe symbol $\\set{3, 4}$ means triangles with four at each corner; this is the octahedron.\nIn four dimensions, $\\set{4, 3, 3}$ means cubes as the three-dimensional cells, with three cubes around each edge; this is the tesseract.\nReading the symbol backwards gives the dual shape, as the cube and the octahedron show.\n",
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