Consider a Knot as being formed from two Tangles. The following three operations are called mutations.

- 1. Cut the knot open along four points on each of the four strings coming out of , flipping over, and gluing the strings back together.
- 2. Cut the knot open along four points on each of the four strings coming out of , flipping to the right, and gluing the strings back together.
- 3. Cut the knot, rotate it by 180°, and reglue. This is equivalent to performing (1), then (2).

**References**

Adams, C. C. *The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots.*
New York: W. H. Freeman, p. 49, 1994.

© 1996-9

1999-05-26