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The knotted hexagon

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Part of the Lecture Notes in Mathematics book series (LNM,volume 622)

Abstract

The knotted and unknotted six-sided polygons in E3 are investigated and the following results established. In order that a set of six points (in general position in E3) be the set of vertices of some knotted hexagon, it is necessary that the convex hull K of the six points have six vertices (i.e. that no point lie inside the convex hull of the other five) and it is necessary and sufficient that K be of a certain combinatorial type, there being two such types all told. There is at most one knotted hexagon which can be formed from any set of six points.

Keywords

  • Line Segment
  • Convex Hull
  • General Position
  • Pure Mathematic
  • Convex Polyhedron

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References

  1. Crowell, R.H., and R.H. Fox, Introduction to Knot Theory, Ginn (Boston) 1963.

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© 1977 Springer-Verlag

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Baddeley, A. (1977). The knotted hexagon. In: Little, C.H.C. (eds) Combinatorial Mathematics V. Lecture Notes in Mathematics, vol 622. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069180

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  • DOI: https://doi.org/10.1007/BFb0069180

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08524-9

  • Online ISBN: 978-3-540-37020-8

  • eBook Packages: Springer Book Archive