The 6-ring

Faniry Razafindrazaka and Konrad Polthier
Proceedings of Bridges 2013: Mathematics, Music, Art, Architecture, Culture (2013)
Pages 279–286 Regular Papers


The 6-ring is a tubular surface of genus 13, obtained by gluing together twenty-four 12-gons which follows the regularity of the map R13.2'{12,3}. It is constructed from six rings of two Borromean rings, has the twenty-four elements of an oriented cube and matches nicely with the 6-coloring of R13.2'{12,3}. The 6-ring has minimal twists and geometrically equivalent sets of four 12-gons. We explicitly construct this highly symmetric surface from two Borromean rings together with a detailed mapping of the 12-gons.