Түйіннің айнасымен сәйкес келмейтін түрі

Knot that is not equivalent to its mirror image
In the mathematical field of knot theory, a chiral knot is a knot that is not equivalent to its mirror image (when identical while reversed). An oriented knot that is equivalent to its mirror image is an amphicheiral knot, also called an achiral knot. The chirality of a knot is a knot invariant. A knot's chirality can be further classified depending on whether or not it is invertible. There are only five knot symmetry types, indicated by chirality and invertibility: fully chiral, invertible, positively amphicheiral noninvertible, negatively amphicheiral noninvertible, and fully amphicheiral invertible.

A chiral knot that can be smoothly deformed to itself with the opposite orientation is classified as a invertible knot. Examples include the trefoil knot.

If a knot is not equivalent to its inverse or its mirror image, it is a fully chiral knot, for example the 9 32 knot.

An amphicheiral knot is one which has an orientation reversing self homeomorphism of the 3 sphere, α, fixing the knot set wise. All amphicheiral alternating knots have even crossing number. The first amphicheiral knot with odd crossing number is a 15 crossing knot discovered by Hoste et al.

If a knot is isotopic to both its reverse and its mirror image, it is fully amphicheiral. The simplest knot with this property is the figure eight knot.

If the self homeomorphism, α, preserves the orientation of the knot, it is said to be positive amphicheiral. This is equivalent to the knot being isotopic to its mirror. No knots with crossing number smaller than twelve are positive amphicheiral and noninvertible .

If the self homeomorphism, α, reverses the orientation of the knot, it is said to be negative amphicheiral. This is equivalent to the knot being isotopic to the reverse of its mirror image. The noninvertible knot with this property that has the fewest crossings is the knot 817.