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.

**References**

J. A. Calvo, *Geometric Knot Theory,* Ph.D. Thesis, Univ. Calif. Santa Barbara, 1998. (For polygons with up to 9 edges.)

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

R. Randell, *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.)