# Stick Number

The stick number of a knot is the minimum number of vertices in a polygonal description of the knot.
Initial data for the table, through 9 crossings, came from Peter Cromwell's book, "Knots and Links,"
where the work of Randell, Negami, and Calvo is credited for the original computations. The references include many values that do not appear in that original source.

## Specific Knots

9_{35},
9_{39},
9_{43},
9_{45},
9_{48}.

Ref. [4]

## References

[1] Calvo, J. A., *Geometric Knot Theory,* Ph.D. Thesis, Univ. Calif. Santa Barbara, 1998.

(For polygons with up to 9 edges.)

[2] Negami, S., "Ramsey theorems for knots, links and spatial graphs," Trans. Amer. Math. Soc. **324** no. 2
(1991), 527-541.

[3] Randell, R., "Invariants of piecewise-linear knots," Knot theory (Warsaw, 1995), 307-319, Banach Center Publ.,
42, Polish Acad. Sci., Warsaw, 1998.

(For polygons with up to 8 edges.)

[4] Eddy, T. D. and Shonkwiler, C., "New stick number Bounds from random sampling of confined polygons," Arxiv preprint.