J. Korean Math. Soc. 2011; 48(2): 367-382
Printed March 1, 2011
https://doi.org/10.4134/JKMS.2011.48.2.367
Copyright © The Korean Mathematical Society.
Youngsik Huh
Hanyang University
We establish a necessary and sufficient condition for a heptagonal knot to be figure-8 knot. The condition is described by a set of Radon partitions formed by vertices of the heptagon. In addition we relate this result to the number of nontrivial heptagonal knots in linear embeddings of the complete graph $K_7$ into $\mathbb{R}^3$.
Keywords: polygonal knot, figure-eight knot, complete graph, linear embedding
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