This archive contains two datasets: Knot128 and Trefoil100. Both datasets are “stress tests” for knot untangling algorithms, i.e., highlytangled configurations that can be difficult to smooth out into a canonical knot embedding. Knot128 is comprised of knots from 128 different isotopy classes; for each class we provide a tangled embedding, and a canonical embedding (for reference). Trefoil100 contains 100 tangled embeddings of the trefoil knot. To date, no algorithm—including ours—succeeds at untangling 100% of these knots (see paper/supplemental for statistics), though we get pretty close!

ZIP, 9.3MB

This archive contains meshes (at several resolutions) of the unknot from the paper “Möbius Energy of Knots and Unknots” by Freedman, He, and Wang, which is used as a performance benchmark in our paper.

ZIP, 1.8MB
