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Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 42, No. 2, pp. 301-306 (2001)
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A New Class of Stuck Unknots in $Pol_6$

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Godfried Toussaint

School of Computer Science, McGill University, 3480 University Street, Montreal, Quebec Canada H3A 2A7 e-mail: godfried@cs.mcgill.ca

**Abstract:** We consider embedding classes of hexagonal unknots with edges of fixed length. Cantarella and Johnston [C] recently showed that there exist "stuck" hexagonal unknots which cannot be reconfigured to convex hexagons for suitable choices of edge lengths. Here we uncover a new class of stuck unknotted hexagons, thereby proving that there exist at least five classes of nontrivial embeddings of the unknot. Furthermore, this new class is stuck in a stronger way than the class described in [C]. \item{[C]} Cantarella, Jason; Johnston, Heather: * Nontrivial embeddings of polygonal intervals and unknots in 3-space.* Journal of Knot Theory and its Ramifications ** 7**(8) (1998), 1027-1039.

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