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Orthogonal Projections Of Lattice Stick Knots, Margaret Marie Allardice

Senior Projects Spring 2016

A lattice stick knot is a closed curve in R³ composed of finitely many line segments, sticks, that lie parallel to the three coordinate axes in R³, such that the line segments meet at points in the 3-dimensional integer lattice. The lattice stick number of a knot is the minimal number of sticks required to realize that knot as a lattice stick knot. A right angle lattice projection is a projection of a knot in R³onto the plane such that the edges of the projection lie parallel to the two coordinate axes in the plane, …