The LooPindex is a digital catalog containing the pinning data of all irreducible, indecomposable multiloops in the unoriented sphere with at most 12 complementary regions. There are a total of 1097 such.
The notations and terminology often follow those introduced in the preprint
Pin the loop taut : a one-player topological game
by Christopher-Lloyd Simon and Ben Stucky, which is available on the arxiv.
The data on these pages is available in flexible formats upon request. The code used to generate everything seen here is available on GitHub.
The multiloops below are unique in that they are the only ones in the catalog with the property that every region has degree at least 3. This property appears to make their minimal pinning sets especially rich.
The multiloops were generated using plantri and they were plotted with SnapPy. We would like to thank Nathan Dunfield who gave us tips for adapting SnapPy to our purposes, as well as Gunnar Brinkmann and Brendan McKay who gave us tips and custom plugins for plantri. The design of the site is inspired by the Knot Atlas.
