Abstract

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 <TEX>$K_7$</TEX> into <TEX>$\mathbb{R}^3$</TEX>.

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