# Wild knot

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In the mathematical theory of knots, a knot is **tame** if it can be "thickened up", that is, if there exists an extension to an embedding of the solid torus *S*^{ 1} × *D*^{ 2} into the 3-sphere. 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. In knot theory and 3-manifold theory, often the adjective "tame" is omitted. Smooth knots, for example, are always tame. Wild knots can be found in some Celtic designs.

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