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# 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

## See also

Link Crossing Number, Triangle Counting

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## 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.

Stick Number

## Cite this as:

Weisstein, Eric W. "Stick Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/StickNumber.html