HEPTAGONAL KNOTS AND RADON PARTITIONS

摘要

We establish a necessary and sufficient condition for a heptagonal knot to befigure-8 knot. The condition is described by a set of Radon partitions formedby vertices of the heptagon. In addition we relate this result to the number ofnontrivial heptagonal knots in linear embeddings of the complete graph $K_7$into $mathbb{R}^3$.