Upper bounds for equilateral stick numbers
upper bounds, equilateral stick numbers
We use algorithms in the software KnotPlot to compute upper bounds for the equilateral stick numbers of all prime knots through 10 crossings, i.e., the least number of equal length line segments it takes to construct a conformation of each knot type. We find seven knots for which we cannot construct an equilateral conformation with the same number of edges as a minimal non-equilateral conformation, notably the 8 19 knot.
Rawdon, E.J. & Scharein, R.G. (2002). Upper bounds for equilateral stick numbers. In Calvo, J.C., Millett, K.C., and Rawdon, E.J., Physical knots: knotting, linking, and folding geometric objects in R^3, (304). 10.1090/conm/304/05184.