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More classes of stuck unknotted hexagons. (English) Zbl 1072.51020
Allowing the vertices of a hexagon \(H\) in \(\mathbb{R}^3\) to move freely as long as the six edges do not cross or deform, the authors study the question how many connected components the space of \(H\) can have (for a suitable choice of the lengths of the edges of \(H\)). E.g., is each connected component of this space corresponding to a separate knot type, or does there exist some knot type (unknot) in separate components of the space? The authors consider the maximum number of embedding classes that any such unknot may have. Continuing respective investigations on hexagons in 3-space, they show that there exists an unknot for hexagons with at least nine embedding classes (before this paper, five was known to be a lower bound).

MSC:
51M20 Polyhedra and polytopes; regular figures, division of spaces
52B10 Three-dimensional polytopes
57M25 Knots and links in the \(3\)-sphere (MSC2010)
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