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 3sphere. 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 3manifold 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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