Abstract
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. While I used this configuration of heptagons to create an eight-color ceramic tea set in 2010 and a bead-crochet eight-color double torus in 2014, both of these designs significantly deformed the eight regions into various shapes conforming to each surface. 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 fabric model with the two holes in roughly perpendicular directions.
