Fran Herr

Topological Crochet Resources

In 2023, I met Shiying Dong who taught me how to make crocheted Seifert surfaces of knots and links. Shiying is a phenomenal crochet artist. Her work has been exhibited at the Joint Math Meetings, the Bridges conference, and the upcoming (2026) International Congress of Mathematics. To get an overview of her work, see this video.

I continue to make models of Seifert surfaces using her techniques. I have also started holding my own topological crochet workshops at U Chicago to teach Shiying's designs. Here are all the resources I know of to learn to make Shiying's designs.

Here is a list of documents written by Shiying which outline instructions for her projects:

• 2025 Bridges paper. An outline of different methods within topological crochet.
• 2024 Bridges paper. Outlines the 2-color method and saddle method in topological crochet. Gives instructions for the saddle trefoil.
• 2023 Bridges paper. Instructions for the Möbius band, Seifert surface of the trefoil knot, and a table of the links resulting from other graphs.
• Document for MoMath workshop series. Instructions for the Möbius band, Seifert surface of the trefoil knot, and surface bounded by the Borromean rings.

For video instructions, see the following:

• My youtube tutorial for the Seifert surface of the trefoil knot. (40 min long)
• My video about designing your own patterns from knot or link diagrams.
• Shiying's youtube channel has several tutorials including for the Möbius band, Seifert surface of the trefoil knot, saddle trefoil, and Borromean rings surface.