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An invertible knot is a knot that can be deformed via an ambient isotopy into itself but with the orientation reversed. A knot that is not invertible is said to be ...

In mathematics, a knot is defined as a closed, non-self-intersecting curve that is embedded in three dimensions and cannot be untangled to produce a simple loop (i.e., the ...

Admitting an inverse. An object that is invertible is referred to as an invertible element in a monoid or a unit ring, or to a map, which admits an inverse map iff it is ...

The stevedore's knot is the 6-crossing prime knot 6_1. It is implemented in the Wolfram Language as KnotData["Stevedore"]. It has braid word ...

The Miller Institute knot is the 6-crossing prime knot 6_2. It is alternating, chiral, and invertible. A knot diagram of its laevo form is illustrated above, which is ...

Solomon's seal knot is the prime (5,2)-torus knot 5_1 with braid word sigma_1^5. It is also known as the cinquefoil knot (a name derived from certain herbs and shrubs of the ...

A knot which is not a tame knot.

The trefoil knot 3_1, also called the threefoil knot or overhand knot, is the unique prime knot with three crossings. It is a (3, 2)-torus knot and has braid word sigma_1^3. ...

The figure eight knot, also known as the Flemish knot and savoy knot, is the unique prime knot of four crossings 04-001. It has braid word ...

An amphichiral knot is a knot that is capable of being continuously deformed into its own mirror image. More formally, a knot K is amphichiral (also called achiral or ...