Knot point constructed on the standing end (such as a loop or overhand knot) into which the working end is easily hitched, using a round turn. An example of this is the bowline. "Constricting" knots often rely on friction to cinch down tight on loose bundles; an example is the Miller's knot. Knots may belong to more than one category. Trick knots are knots that are used as part of a magic trick, a joke, or a puzzle. They are useful for these purposes because they have a deceptive appearance, being easier or more difficult to tie or untie than their
Mutation (knot theory) endpoints of the tangle. There is also a rotation that results from composition of the reflections. A mutation replaces the original tangle by a tangle given by any of these operations. The result will always be a knot and is called a mutant of "K". Mutants can be difficult to distinguish as they have a number of the same invariants. They have the same hyperbolic volume (by a result of Ruberman), and have the same HOMFLY polynomials. Mutation (knot theory) In the mathematical field of knot theory, a mutation is an operation on a knot that can produce different knots.