Polygonal Knot

A knot equivalent to a polygon in R^3, also called a tame knot. For a polygonal knot K, there exists a plane such that the orthogonal projection pi on it satisfies the following conditions:

1. The image pi(K) has no multiple points other than a finite number of double points.

2. The projections of the vertices of K are not double points of pi(K).

Such a projection pi(K) is called a regular knot projection.

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Iyanaga, S. and Kawada, Y. (Eds.). Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 735, 1980.

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Polygonal Knot

Cite this as:

Weisstein, Eric W. "Polygonal Knot." From MathWorld--A Wolfram Web Resource.

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