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
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
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