FIGURE-8 KNOT ON THE CUBIC LATTICE

Abstract

We will examine the stick number of knots on the cubic lattice which is called the lattice stick number. The lattice stick numbers of knots <TEX>$3_1$</TEX> and <TEX>$4_1$</TEX> are known as 12 and 14, respectively. In this paper, we will show that only <TEX>$3_1$</TEX> and <TEX>$4_1$</TEX> have representations of irreducible non-trivial polygons, both numbers of whose sticks parallel to the y-axis and the z-axis are exactly four.