Stick Number

Let the stick number  of a knot  be the least number of straight sticks needed to make a knot . The smallest stick number of any knot is , where  is the trefoil knot. If  and  are knots, then

For a nontrivial knot , let  be the link crossing number (i.e., the least number of crossings in any projection of ). Then

Stick numbers are implemented in the Wolfram Language as KnotData[knot, "StickNumber"].

The following table gives the stick number for knots on 10 or fewer crossings.

	3		9		11		12		11		12		11		11		10
	6		9		10		12		12		11		12		10		10
	7		9		11		12		12		12		11		10		10
	8		8		10		11		13		11		11		10		10
	8		8		9		12		11		12		12		10		10
	8		9		10		11		11		12		12		11		10
	8		10		10		11		11		12		10		10		10
	8		11		10		11		12		13		11		11		10
	9		11		10		11		12		12		10		10		11
	9		10		9		12		11		12		12		10		10
	9		10		10		11		12		13		11		10
	9		11		11		11		12		12		10		11
	9		10		10		12		10		12		10		11
	9		10		10		11		11		11		10		10
	9		10		10		12		12		13		12		10
	10		10		9		12		12		11		11		10
	10		11		9		12		11		12		11		11
	10		10		9		12		12		11		10		11
	10		10		10		12		12		14		10		10
	10		10		9		11		12		11		11		10
	10		11		10		12		11		11		10		10
	10		10		9		11		12		11		12		10
	10		10		9		12		12		11		11		11
	10		11		10		11		11		11		10		11
	10		10		9		12		11		11		10		10
	10		10		11		12		11		11		10		10
	10		11		11		11		12		11		10		11
	10		10		12		11		11		11		11		11
	10		11		11		12		13		11		10		11
	10		10		11		12		12		12		10		10

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.