Knots & Links on the Cubic Lattice
Marnie Phipps · TopSCHOLAR (Western Kentucky University) · 1999
The cubic lattice is a graph in R3 whose vertices are all points with coordinates (x, y, z) where x, y, and z are integers and whose edges are of unit length where they are line segments connecting the vertices. This thesis addresses how many edges of the cubic lattice are needed to realize a given knot or link. The main theorem proves that a four crossing link, denoted 4 2/I, needs a minimum of 28 edges. In addition the number of edges needed to realize a family of knot, called (p, 2) torus knots, is given.