Figure-eight knot (mathematics)

In knot theory, a figure-8 knot is the unique knot with a crossing number of four, the smallest possible except for the unknot and trefoil knot. The name is given because joining the ends of a string with a normal figure-8 knot tied in it, in the most natural way, gives a model of the mathematical knot.

A simple representation of the figure-8 knot is as the set of all points (x,y,z) where

x = (2 + cos(2t)) cos(3t)
y = (2 + cos(2t)) sin(3t)
z = sin (4t)

for some real value of t. The knot is alternating, rational with an associated value of 5/2, and is achiral. It is also the hyperbolic knot whose complement has the largest possible volume, 2.02988...