Category:Hyperbolic knots and links

Every knot is precisely one of the following: hyperbolic, a torus knot, or a satellite knot.

Every non-split, prime, alternating link that is not a torus link is hyperbolic by a result of William Menasco.

"Of the prime knots with 16 or fewer crossings, all but 32 are hyperbolic. Of these 32, 12 are torus knots and the remaining 20 are satellites of the trefoil knot (Hoste et al. 1998)."