# Showing pass equivalence of cinquefoil knot

According to C.C. Adams, The knot book, pp 224, "every knot is either pass equivalent to the trefoil knot or the unknot".

A pass move is the following:

Can someone show me how to show that the Cinquefoil knot is pass equivalent to unknot or trefoil? Been trying on paper but no luck. Don't see how pass moves apply here. Thanks.

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Using Reidemeister moves would also be ok, have also tried that, also no success. – Rudy the Reindeer Sep 6 '12 at 12:28

The general method is demonstrated in Kauffman's book On Knots. Put the knot into a "band position" So that the Seifert surface is illustrated as a disk with twisted and intertangled bands attached. Then the orientations match those of your figure. You can pass one band over another. Your knot is the braid closure of $\sigma_1^5$. The Seifert surface is two disks with 5 twisted bands between them. Start by stretching the disks apart.