Chiral knot

Mary Gertrude Haseman found all 12-crossing and many 14-crossing amphicheiral knots in the late 1910s.

[3][4] But a counterexample to Tait's conjecture, a 15-crossing amphicheiral knot, was found by Jim Hoste, Morwen Thistlethwaite, and Jeff Weeks in 1998.

[5] However, Tait's conjecture was proven true for prime, alternating knots.

No knots with crossing number smaller than twelve are positive amphicheiral and noninvertible .

[8] If the self-homeomorphism, α, reverses the orientation of the knot, it is said to be negative amphicheiral.

The figure-eight knot is the simplest amphicheiral knot.
The first negative amphicheiral knot.