Pretzel link

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P(5,3,-2) = T(5,3) = 10₁₂₄

P(3,3,-2) = T(4,3) = 8₁₉

Only two knots are both torus and pretzel^[1]

In the mathematical theory of knots, a pretzel link is a special kind of link. It consists of a finite number of tangles made of two intertwined circular helices. The tangles are connected cyclicly,^[2] and the first component of the first tangle is connected to the second component of the second tangle, the first component of the second tangle is connected to the second component of the third tangle, and so on. Finally, the first component of the last tangle is connected to the second component of the first. A pretzel link which is also a knot (that is, a link with one component) is a pretzel knot.

Each tangle is characterized by its number of twists: positive if they are counter-clockwise or left-handed, negative if clockwise or right-handed. In the standard projection of the ${\displaystyle (p_{1},\,p_{2},\dots ,\,p_{n})}$ pretzel link, there are ${\displaystyle p_{1}}$left-handed crossings in the first tangle, ${\displaystyle p_{2}}$in the second, and, in general, ${\displaystyle p_{n}}$in the nth.

A pretzel link can also be described as a Montesinos link with integer tangles.