Knot Diagram

A picture of a projection of a Knot onto a Plane. Usually, only double points are allowed (no more than two points are allowed to be superposed), and the double or crossing points must be ``genuine crossings'' which transverse in the plane. This means that double points must look like the below diagram on the left, and not the one on the right.

$\begin{figure}\begin{center}\BoxedEPSF{KnotDiagrams.epsf scaled 1400}\end{center}\end{figure}$

Also, it is usually demanded that a knot diagram contain the information if the crossings are overcrossings or undercrossings so that the original knot can be reconstructed. Here is a knot diagram of the Trefoil Knot,

$\begin{figure}\begin{center}\BoxedEPSF{Trefoil_Knot.epsf}\end{center}\end{figure}$

Knot Polynomials can be computed from knot diagrams. Such Polynomials often (but not always) allow the knots corresponding to given diagrams to be uniquely identified.