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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