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  "body": "\n## Summary\n\nA satellite knot is a [[knot|QYEAZTYGPT]] that lies inside a thickened copy of another nontrivial knot, the companion, in an essential way.\nEquivalently, its complement contains an incompressible torus that is not parallel to the boundary.\nSatellite knots form one of the three classes in Thurston's division of knots, with [[torus knots|NS60VV786W]] and [[hyperbolic knots|K47G2Q24DT]].\nEvery [[knot sum|AGZSZW7GYE]] of two nontrivial knots is a satellite knot.\n\n## Explanations\n\n### L1 human\n\nTake a nontrivial knot and thicken it into a knotted tube.\nNow draw a new knot inside the tube, one that winds through the tube and cannot be pulled out of it or shrunk to a small ball inside it.\nThe new knot is a satellite, and the old knot is its companion.\nCables, where the new knot winds around the tube several times, are a simple example.\nThe granny knot, the sum of two trefoils, is a satellite with a trefoil as companion.\n",
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  "name": "Satellite knot",
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