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Twist Knot

TwistKnots

Given a doubled knot with the unknot taken as the base knot K_1, the companion knot K_2 of K_1 is called a twist knot with q twists. As illustrated above, the following knots are twist knots (Rolfsen 1976, p. 112).

qknot
-1trefoil knot
1figure eight knot
2stevedore's knot

The unknot and stevedore's knot are the only twist knots that are slice knots (Casson and Gordon 1975; Rolfsen 1976, p. 226).

See also

Cable Knot, Companion Knot, Doubled Knot, Satellite Knot, Slice Knot

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References

Casson, J. and Gordon, C. M. "Cobordism of Classical Knots." Preprint of Lecture. Orsay. 1975.Rolfsen, D. Knots and Links. Wilmington, DE: Publish or Perish Press, p. 112, 1976.

Referenced on Wolfram|Alpha

Twist Knot

Cite this as:

Weisstein, Eric W. "Twist Knot." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TwistKnot.html

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