LATTICE STICK NUMBERS OF SMALL KNOTS

Abstract

Lattice stick number s L (K) is defined to be the minimal number of sticks required to construct a polygonal representation of the knot K in the cubic lattice. In this paper, we give lattice stick numbers of small knots such as 3 1 and 4 1 . More precisely we prove that s L (3 1 ) = 12 and s L (K) ≥ 14 for any other non-trivial knot K.