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Also called the Tait Flyping Conjecture. Given two reduced alternating projections of the same knot, they are equivalent on the Sphere Iff they are related by a series of Flypes. It was proved by Menasco and Thistlethwaite (1991). It allows all possible Reduced alternating projections of a given Alternating Knot to be drawn.
References
Adams, C. C. The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots.
New York: W. H. Freeman, pp. 164-165, 1994.
Menasco, W. and Thistlethwaite, M. ``The Tait Flyping Conjecture.'' Bull. Amer. Math. Soc. 25, 403-412, 1991.
Stewart, I. The Problems of Mathematics, 2nd ed. Oxford, England: Oxford University Press, pp. 284-285, 1987.