Файл:12crossings-rose-rhodonea-limacon-symmetrical-knot.svg

Decorative knot with twelve crossings, depicted with three-fold visual symmetry. The curves were generated from the polar coordinates equation r=b+sin(aθ), which is a slight generalization of the Limaçon and Rose/rhodonea curves, using parameters a=(3/5) and b=(3/2).

If the three outermost curve segments which directly connect the three outer crossings are deleted, and the lines which intersect at these three outer crossings are joined together there, then you get the 9-crossing knot seen in image File:Knot-9crossings-symmetrical.svg.

If everything outside of the three next-to-outermost crossings is deleted, and the lines which intersect at these three crossings are joined together there, then you get the Borromean rings configuration.

If everything outside of the three next-to-inner crossings is deleted, and the lines which intersect at these three crossings are joined together there, then you get a Triquetra (topologically equivalent to a Trefoil knot).

If everything outside of the three innermost crossings is deleted, and the lines which intersect at these three crossings are joined together there, then you get a form of triangle (topologically equivalent to a simple circle or closed loop, i.e. "unknot").

Self-made graphic, converted from the following vector PostScript source code:

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