Pretzel Notation

A pretzel knot is formed from a planar unlink of two components by joining the two components with parallel twisted bands. For instance, P(-2,3,7) is formed by adding bands with -2, 3, and 7 half twists as illustrated below. The diagram presents P(-2,3,7). (This knot is also 12n242.)

Pretzel Example

The data through 9 crossings was provided by Diaz and Manchon [1], who checked that it is correct with respect to orientation.

Specific Knots



[1] Diaz, R. and P. M. G. Manchon, P. M. G., "Pretzel knots up to nine crossings," Arxiv preprint.