Geometriae Dedicata

, Volume 154, Issue 1, pp 27–46 | Cite as

Conformal hexagonal meshes

  • Christian MüllerEmail author
Original Paper


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.


Discrete differential geometry Hexagonal mesh Discrete conformal map Discrete Christoffel duality Discrete minimal surface Elementary geometry 

Mathematics Subject Classification (2000)

51M04 52C26 52C99 53A40 


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Institute of Discrete Mathematics and Geometry, TU WienViennaAustria

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