Prime knots and links

simplest non-trivial closed knot with three crossings

right|150px|thumb|Two simple diagrams of the unknot In the mathematical theory 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 into it, unknotted. To a knot theorist, an unknot is any embedded topological circle in the 3-sphere that is ambient isotopic (that is, deformable) to a geometrically round circle, the standard unknot.

prime link; simplest nontrivial link

unique knot with a crossing number of four

non-trivial knot which cannot be written as the knot sum of two non-trivial knots

prime knot with 11 crossings named for John Horton Conway

two interlinked loops with five structural crossings

torus knot with crossing number 5

mathematical knot with crossing number 6

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mathematical knot with crossing number 5

mathematical knot with crossing number 7