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# Three-twist knot

In knot theory, the three-twist knot is the twist knot with three-half twists. [1]

## Alexander polynomial

In mathematics, the Alexander polynomial is a knot invariant which assigns a polynomial with integer coefficients to each knot type.

## Chiral knot

In the mathematical field of knot theory, a chiral knot is a knot that is not equivalent to its mirror image.

## Cinquefoil knot

In knot theory, the cinquefoil knot, also known as Solomon's seal knot or the pentafoil knot, is one of two knots with crossing number five, the other being the three-twist knot.

## Crossing number (knot theory)

In the mathematical area of knot theory, the crossing number of a knot is the smallest number of crossings of any diagram of the knot.

## Fibered knot

In knot theory, a branch of mathematics, a knot or link K in the 3-dimensional sphere S^3 is called fibered or fibred (sometimes Neuwirth knot in older texts, after Lee Neuwirth) if there is a 1-parameter family F_t of Seifert surfaces for K, where the parameter t runs through the points of the unit circle S^1, such that if s is not equal to t then the intersection of F_s and F_t is exactly K. For example.

In mathematics, a hyperbolic link is a link in the 3-sphere with complement that has a complete Riemannian metric of constant negative curvature, i.e. has a hyperbolic geometry.

## Hyperbolic volume

In the mathematical field of knot theory, the hyperbolic volume of a hyperbolic link is the volume of the link's complement with respect to its complete hyperbolic metric.

## Invertible knot

In mathematics, especially in the area of topology known as knot theory, an invertible knot is a knot that can be continuously deformed to itself, but with its orientation reversed.

## Jones polynomial

In the mathematical field of knot theory, the Jones polynomial is a knot polynomial discovered by Vaughan Jones in 1984.

## Knot theory

In topology, knot theory is the study of mathematical knots.

## Monic polynomial

In algebra, a monic polynomial is an univariate polynomial in which the leading coefficient (the nonzero coefficient of highest degree) is equal to 1.

## Prime knot

In knot theory, a prime knot or prime link is a knot that is, in a certain sense, indecomposable.

## Twist knot

In knot theory, a branch of mathematics, a twist knot is a knot obtained by repeatedly twisting a closed loop and then linking the ends together.

## References

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