Stuck unknot

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In mathematics, a stuck unknot is a polygonal closed loop that is topologically the unknot but cannot be simplified to a planar polygon by rigid motions of the segments.[1][2] A related idea is to consider "stuck" polygonal open chains[disambiguation needed]. Topologically these chains can be unknotted, but the limitation of using only rigid motions of the segments can create nontrivial knots in such a chain.

Consideration of such "stuck" configurations arises in the study of molecular chains in biochemistry.


  1. ^ G. Aloupis, G. Ewald, and G. T. Toussaint, "More classes of stuck unknotted hexagons," Contributions to Algebra and Geometry, Vol. 45, No. 2, 2004, pp. 429–434.
  2. ^ G. T. Toussaint, "A new class of stuck unknots in Pol-6," Contributions to Algebra and Geometry, Vol. 42, No. 2, 2001, pp. 301–306.