Conformal hexagonal meshes

C. Müller


We explore discrete conformal and discrete minimal surfaces whose faces are planar hexagons throughout. Discrete conformal meshes are built of conformal hexagons for which we establish a dual construction. We apply this dual construction to conformal hexagonal meshes covering the sphere and get discrete hexagonal minimal surfaces via a discrete analogue to the Christoffel dual construction.We compare the smooth and the discrete
settings by means of limit considerations and also by a discussion of Möbius invariants.


   author = {M{\"u}ller, Christian},
   title = {Conformal hexagonal meshes},
   journal = {Geometriae Dedicata},
   publisher = {Springer Netherlands},
   issn = {0046-5755},
   pages = {27-46},
   volume = {154},
   issue = {1},
   doi = {},
   url = "",
   year = {2011}