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.
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.)