The noncommutative geometry of wire networks from triply periodic   surfaces
  We study wire networks that are the complements of triply periodic minimal surfaces. Here we consider the P, D, G surfaces which are exactly the cases in which the corresponding graphs are symmetric and self-dual. Our approach is using the Harper Hamiltonian in a constant magnetic field. We treat this system with the methods of noncommutative geometry and obtain a classification for all the $C^*$ geometries that appear. 
Ralph M. Kaufmann, Sergei Khlebnikov and Birgit Wehefritz-Kaufmann
math-ph math.MP