Wild knot

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 tame if and only if it can be represented as a finite closed polygonal chain.

Knots that are not tame are called wild and can have pathological behavior.

[1] It has been conjectured that every wild knot has infinitely many quadrisecants.

[2] As well as their mathematical study, wild knots have also been studied for their potential for decorative purposes in Celtic-style ornamental knotwork.