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  "body": "\n## Summary\n\nA vertex of a [[convex polytope|300K6CB1KH]] is a [[face|KY7SB854VH]] of dimension zero, that is, a corner point of the polytope.\nVertices are exactly the [[extreme points|3MSGFJM2NX]] of the polytope: the points that are not inside a segment between two other points of it.\nA convex polytope is the [[convex hull|0FQSDC2EQ2]] of its vertices, and no smaller set of points has this hull.\nSo the vertices form the most economical description of a polytope, the V-description.\n\n## Explanations\n\n### L1 human\n\nThe vertices of a polytope are its corners.\nA square has four, a cube has eight, a tetrahedron has four.\nAt a vertex you can tilt a flat plane so that it touches the solid at that point only.\nIf you know the corners, you know the whole solid: stretch a skin tightly around them and it gives the polytope back.\n",
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