A decade ago, in search of a versatile eight-color map on a double torus, I discovered an intriguing gluing of eight heptagons. Topologically, the glued heptagons form a surface of genus two on which each heptagon shares a border with each of the others, demonstrating that at least eight colors are required to color an arbitrary map on a double torus. I used this heptagonal framework in double-torus artworks in 2010 and 2014, but the original heptagons were distorted beyond recognition. This paper shows what happened when I stitched together eight congruent crocheted heptagons into the double-torus map, an endeavor I first attempted this year.

The result is a delightfully twisted flexible fabric model with the two holes in roughly perpendicular directions. My companion website includes video of the object, which you can crochet yourself from my supplementary pattern file in the Bridges 2020 archive.