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  "body": "\n## Summary\n\nA hyperbolic knot is a [[knot|QYEAZTYGPT]] whose complement in the $3$-sphere carries a complete hyperbolic metric of finite volume.\nBy Mostow–Prasad rigidity this metric is unique, so its volume and other geometric quantities are knot invariants.\nThurston showed that every nontrivial knot is a [[torus knot|NS60VV786W]], a [[satellite knot|A1E8TDEVJ9]] or a hyperbolic knot, and exactly one of these.\nMost knots in the tables are hyperbolic.\n\n## Explanations\n\n### L1 human\n\nRemove a knot from space and study the space that is left over.\nFor a hyperbolic knot, that leftover space can be given the geometry of the hyperbolic plane, raised to three dimensions, in which triangles have angle sums below $180$ degrees.\nThis geometry is rigid, so its total volume is a number attached to the knot.\nThe [[figure-eight knot|C01XBGAHC6]] is hyperbolic, and its complement has volume about $2.0299$.\nThe trefoil is not hyperbolic, because it is a torus knot.\n",
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