Stick Number

Let the stick number $s(K)$ of a Knot $K$ be the least number of straight sticks needed to make a Knot $K$. The smallest stick number of any Knot is $s(T)=6$, where $T$ is the Trefoil Knot. If $J$ and $K$ are Knots, then

$$s(J+K)\leq s(J)+s(K)+1.$$

For a nontrivial Knot $K$, let $c(K)$ be the Crossing Number (i.e., the least number of crossings in any projection of $K$). Then

$${\textstyle{1\over 2}}[5+\sqrt{25+8(c(K)-2)}]\leq s(K)\leq 2c(K).$$

The following table gives the stick number for some common knots.

Trefoil Knot	6
Whitehead Link	8

See also Crossing Number (Link), Triangle Counting

References

Adams, C. C. The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots. New York: W. H. Freeman, pp. 27-30, 1994.