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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,


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.

© 1996-9 Eric W. Weisstein