Square knot (mathematics)

In knot theory, the square knot is a composite knot obtained by taking the connected sum of a trefoil knot with its reflection. It is closely related to the granny knot, which is also a connected sum of two trefoils. Because the trefoil knot is the simplest nontrivial knot, the square knot and the granny knot are the simplest of all composite knots.

Square knot
Three-dimensional view
Common name	Reef knot
Crossing no.	6
Stick no.	8
A–B notation	${\displaystyle 3_{1}\#3_{1}^{*}}$
Other
alternating, composite, pretzel, slice, amphichiral, tricolorable

The square knot is the mathematical version of the common reef knot.