# Polygon Index

The polygon 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.

## 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.