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In knot theory, the cinquefoil knot, also known as Solomon's seal knot or the pentafoil knot, is one of two knots with crossing number five, the other being the three-twist knot. It is listed as the 51 knot in the Alexander-Briggs notation, and can also be described as the (5,2)-torus knot. The cinquefoil is the closed version of the double overhand knot.
The cinquefoil is a prime knot. Its writhe is 5, and it is invertible but not amphichiral. Its Alexander polynomial is
,
its Conway polynomial is
,
and its Jones polynomial is
Surprisingly, these are the same as the Alexander, Conway, and Jones...