Invertible knot information

as knot theory, an invertible knot is a knot that can be continuously deformed to itself, but with its orientation reversed. A non-invertible knot is...

whether or not it is invertible. There are only five knot symmetry types, indicated by chirality and invertibility: fully chiral, invertible, positively amphicheiral...

trefoils are not ambient isotopic.) Though chiral, the trefoil knot is also invertible, meaning that there is no distinction between a counterclockwise-oriented...

double torus (a genus 2 surface). Fibered knot Framed knot Invertible knot Prime knot Legendrian knot are knots embedded in R 3 {\displaystyle \mathbb {R}...

pretzel knot is a non-invertible knot. The (2p, 2q, 2r) pretzel link is a link formed by three linked unknots. The (−3, 0, −3) pretzel knot (square knot (mathematics))...

closed version of the double overhand knot. The cinquefoil is a prime knot. Its writhe is 5, and it is invertible but not amphichiral. Its Alexander polynomial...

In topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope,...

In knot theory, the 62 knot is one of three prime knots with crossing number six, the others being the stevedore knot and the 63 knot. This knot is sometimes...

crossing number seven. It is the simplest torus knot after the trefoil and cinquefoil. The 71 knot is invertible but not amphichiral. Its Alexander polynomial...

and knot theory. In 1963, he solved an open problem in knot theory by proving that there are non-invertible knots. At the time of his proof, all knots with...

In knot theory, a prime knot or prime link is a knot that is, in a certain sense, indecomposable. Specifically, it is a non-trivial knot which cannot...

In knot theory, a torus knot is a special kind of knot that lies on the surface of an unknotted torus in R3. Similarly, a torus link is a link which lies...

All twist knots are invertible, but the only amphichiral twist knots are the unknot and the figure-eight knot. The invariants of a twist knot depend on...

is also invertible, meaning that orienting the curve in either direction yields the same oriented knot. The Alexander polynomial of the 63 knot is Δ (...

of knots, the unknot, not knot, or trivial knot, is the least knotted of all knots. Intuitively, the unknot is a closed loop of rope without a knot tied...

In mathematical knot theory, 74 is the name of a 7-crossing knot which can be visually depicted in a highly-symmetric form, and so appears in the symbolism...

A slice knot is a mathematical knot in 3-dimensional space that bounds an embedded disk in 4-dimensional space. A knot K ⊂ S 3 {\displaystyle K\subset...

finished with an inverted half hitch. A dead turn We cross by making an eight Prepare the reverse half hitch The finished knot List of knots Cleat Clove hitch...

In mathematics, in particular in knot theory, the Conway knot (or Conway's knot) is a particular knot with 11 crossings, named after John Horton Conway...

mathematicians have tried to classify and tabulate all possible knots. As of May 2008, all prime knots up to 16 crossings have been tabulated. The major challenge...

In the mathematical field of knot theory, the tricolorability of a knot is the ability of a knot to be colored with three colors subject to certain rules...

mathematical field of knot theory, a knot invariant is a quantity (in a broad sense) defined for each knot which is the same for equivalent knots. The equivalence...

In the mathematical theory of knots, a knot is tame if it can be "thickened", that is, if there exists an extension to an embedding of the solid torus...

a knot is an embedding of a circle into 3-dimensional Euclidean space. The knot group of a knot K is defined as the fundamental group of the knot complement...