Capturing Eight-Color Double-Torus Maps

Susan Goldstine
Proceedings of Bridges 2014: Mathematics, Music, Art, Architecture, Culture (2014)
Pages 377–380


The extensions of the Four-Color Map Theorem to surfaces of higher genus are difficult to visualize. For instance, without a physical model of a torus map with seven pairwise adjacent countries, it is hard to imagine that there are maps on a torus that require seven colors to color all the countries so that no adjacent countries are the same color. Making maps with large numbers of pairwise adjacent countries is a delightful artistic challenge that lends itself to a variety of media. Here, we present a scheme to produce a map that requires the maximum eight colors on a two-holed torus and show two artworks made with that scheme: a painted ceramic tea set and a bead crochet pendant.