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The problem of deciding if two knots in three-space are equivalent such that one can be continuously deformed into another.

An unknot which can only be unknotted by first increasing the number of crossings.

A single component algebraic link. Most knots up to 11 crossings are algebraic, but they quickly become outnumbered by nonalgebraic knots for more crossings (Hoste et al. ...

In general, it is possible to link two n-dimensional hyperspheres in (n+2)-dimensional space in an infinite number of inequivalent ways. In dimensions greater than n+2 in the ...

A simple way to describe a knot projection. The advantage of this notation is that it enables a knot diagram to be drawn quickly. For an oriented alternating knot with n ...

There are 432 enantiomorphous and 415 chiral fully supported stellations of the icosidodecahedron. Using Miller's rules gives 7071672 enantiomorphous stellations and an ...

Let a knot K be n-embeddable. Then its tunnel number is a knot invariant which is related to n.

The clove hitch is the hitch illustrated above that is also called the boatman's knot or peg knot.

A knot used to shorten a long rope.

Two knots are pass equivalent if there exists a sequence of pass moves taking one to the other. Every knot is either pass equivalent to the unknot or trefoil knot. These two ...