A knot mutation is the operation of cutting a knot along a Conway sphere, rotating one of the resulting tangles through 
, and regluing it. Up
to isotopy, the three mutually perpendicular axes of rotation give three types of
mutation. The rotation preserves the set of four points where the knot meets the
Conway sphere, so mutating a knot produces another knot rather than a link.
A mutation applied to an alternating knot projection yields another alternating knot projection.
