Eight-Color 8

The Four-Color Theorem says that we can color any map on a plane or sphere with only four colors so that no neighboring countries are the same color. On other surfaces, we may need more colors; on a two-holed torus, eight colors are sufficient, and there are maps that require all eight colors.

This beaded pendant shows a map with eight countries, each of which touches all of the others, an impossible feat on a one-holed torus or a sphere. The ornamental silver bead is a purely aesthetic accent that exploits an unavoidable asymmetry in the eight interlocking spirals around the middle of the 8. The pendant was crocheted in a single piece with 797 beads and then joined with two circular seams, one on each side of the thicker central section.

My Bridges 2014 proceedings paper Capturing Eight-Color Double-Torus Maps describes the design process for the pendant.