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  "body": "\n## Summary\n\nA simple polytope is a [[convex polytope|300K6CB1KH]] of dimension $d$ in which every [[vertex|R7V3S9V891]] lies on exactly $d$ edges.\nNear each vertex it then looks like the corner of a cube.\nSimple polytopes are the duals of [[simplicial polytopes|YVJ15PGKDM]], so results about one class translate into results about the other.\nPolytopes given by inequalities in general position are simple, which makes them the generic case in linear programming.\n\n## Explanations\n\n### L1 human\n\nAt each corner of a cube exactly three edges meet, and the cube lives in three dimensions.\nA polytope with this property at every corner, in any dimension, is called simple.\nThe square pyramid is not simple: four edges meet at its apex.\nIf you slightly shift the walls of any polytope in a random way, the result is simple.\n",
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