Polygonal knots

Abstract

We have known that the polygonal index of a tame knot is a knot invariant. In this thesis, we show that every nontrivial knot has polygon index not smaller than 6 and give some estimations of the polygon indices of torus knots $T_{r,s}$, whitehead doubles of the unknot having n crossings $W_n$, pretzel links $Sigma(a_1, a_2$,…,$a_n$) and connected sums p#$\iota$.