Perko pair - What's the handedness of these pictures?

The diagrams in On the Classification of Knots are left-handed.

The pictures from KnotPlot are left-handed.

Wikipedia's pictures are right-handed.

The first of Perko's drawings is right-handed; the second is left-handed.

I determined this experimentally by tying the knots in my headphones and manipulating them until I got them into a form I recognized. I didn't compute the Jones polynomials, since that would probably take around an hour per knot.

This was much harder than I thought it would be. I thought that a physical knot would naturally end up in the configuration of "lowest energy" (whatever that means) when the ends are pulled, but it turns out that knots are much more annoying than that.

I have a lot of respect for the early knot theorists who made knot tables before anyone knew how to rigorously prove that any two knots were distinct. And I don't blame them for thinking the Perko pair was two distinct knots.

Here's the (left-handed) Perko knot tied in my headphones: https://imgur.com/a/OC3TAkH


The sign of the writhe of any 10-crossing diagram (the sum of the signs of the crossings, which must be either + or - 10 or 8 for the Perko pair knot) will show the handedness of any particular drawing. It's no big deal.

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