A Turk's head knot is a Turk's head link 
with relatively prime
positive parameters 
and 
.
It is therefore a one-component closure of the alternating braid 
.
For 
,
the braid is trivial. The cases 
and 
are a trefoil knot and
the figure eight knot, respectively (Di Prisa
and Savk 2026).
Turk's Head Knot
See also
Braid, Turk's Head LinkExplore with Wolfram|Alpha
References
Di Prisa, A. and Savk, O. "Turk's Head Knots and Links: A Survey." Expo. Math. 44, 125777, 2026. https://doi.org/10.1016/j.exmath.2026.125777.Cite this as:
Weisstein, Eric W. "Turk's Head Knot." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TurksHeadKnot.html