Stick number

Known values

Six is the lowest stick number for any nontrivial knot. There are few knots whose stick number can be determined exactly. Gyo Taek Jin determined the stick number of a ${\displaystyle (p,q)}$-torus knot ${\displaystyle T(p,q)}$ in case the parameters ${\displaystyle p}$ and ${\displaystyle q}$ are not too far from each other:

${\displaystyle \mathrm{stick}(T(p,q))=2q}$, if ${\displaystyle 2\le p<q\le 2p.}$

The same result was found independently around the same time by a research group around Colin Adams, but for a smaller range of parameters.