Every knot has a description as a polygon, determined by a finite sequence of vertices in three-space and formed by joining successive vertices by line segments. The stick number of a knot is the minimum number of vertices in such a polygonal description of the knot. Initial data for the table, through 9 crossings, came from [2], where the work of [1], [4], and [5] is credited for the original computations. The references include many values that do not appear in that original source.

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

Ref. [3]

9_{18},
10_{18},
10_{68},
10_{82},
10_{84},
10_{93},
10_{100},
10_{152}.

Upper bounds of 10. Ref. [6]

10_{58},
10_{66},
10_{79},
10_{80}.

Upper bounds of 11. Ref. [6]

11n_{72},
12n_{553}.

Upper bounds of 11. Ref. [7]

11n_{77},
12n_{60},
12n_{219}.

Upper bounds of 12. Ref. [7]

12n_{66},
12n_{225}.

Upper bounds of 13. Ref. [7]

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

(For polygons with up to 9 edges.)

[2] Cromwell, P., *Knots and Links,* Cambridge University Press, 2004.

[3] Eddy, T. D. and Shonkwiler, C., "New stick number Bounds from random sampling of confined polygons," Experimental Math., DOI: 10.1080/10586458.2021.1926000. Arxiv preprint.

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

[5] 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.)

[6] Shonkwiler, C., "All prime knots through 10 crossings have superbridge Index ≤ 5," J. Knot Theory Ramifications, DOI: 10.1142/S0218216522500237. Arxiv preprint.

[7] Shonkwiler, C., "New superbridge index calculations from non-minimal realizations." Arxiv preprint.