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Polygonal knot

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A polygonal knot is a knot whose image in 
 3
is the union of a finite set of line segments.[1] A tame knot is any knot equivalent to a polygonal knot.[1][2] Knots which are not tame are called wild knots,[3] and can have pathological behavior.[3] In knot theory and 3-manifold theory, often the adjective "tame" is omitted. Smooth knots, for example, are always tame.

Notes

  1. 1.0 1.1 (Armstrong 1983), p. 215.
  2. A knot is tame if and only if it can be represented as a finite closed polygonal chain.
  3. 3.0 3.1 (Livingstone 1996), Section 2.1 Wild Knots and Unknottings, pp. 11–14.