thumb|right|A tricolored trefoil knot.In the mathematical field of knot theory, the tricolorability of a knot is the ability of a knot to be colored with three colors subject to certain rules. Tricolorability is an isotopy invariant, and hence can be used to distinguish between two different (non-isotopic) knots. In particular, since the unknot is not tricolorable, any tricolorable knot is necessarily nontrivial.
thumb|right|A tricolored trefoil knot.In the mathematical field of knot theory, the tricolorability of a knot is the ability of a knot to be colored with three colors subject to certain rules. Tricolorability is an isotopy invariant, and hence can be used to distinguish between two different (non-isotopic) knots. In particular, since the unknot is not tricolorable, any tricolorable knot is necessarily nontrivial.
==Rules of tricolorability== In these rules a strand in a knot diagram will be a piece of the string that goes from one undercrossing to the next. A knot is tricolorable if each strand of the knot diagram can be colored one of three colors, subject to the following rules: 1. At least two colors must be used, and 2. At each crossing, the three incident strands are either all the same color or all different colors.
Discovered by embedding cosine similarity (sentence-transformers MiniLM, 384-dim).