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.
