The Journal of Geometric Analysis

, Volume 15, Issue 3, pp 425–443 | Cite as

Soap films and Kelvin's curved, truncated octahedron



Here, the Weierstrass representation theorem for minimal surfaces is used to derive parametrizations of two soap films spanning a rectangular prism with square base. The parametrizations are explicit, although the exact values of the height of the prism and the edge length of the square base can only be determined numerically from the formulas. The more famous of these two soap films can be extended to a partition of ℝ3 by curved, truncated octahedra. Furthermore, if the height of the prism is taken to be\(1/\sqrt 2 \), then the partition is that discovered by Lord Kelvin in the late 19th century.

Math Subject Classifications

Primary: 49Q05 secondary: 32G15 

Key Words and Phrases

Minimal surface flat structure soap film triply periodic Kelvin 


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Copyright information

© Mathematica Josephina, Inc. 2005

Authors and Affiliations

  1. 1.Indiana UniversityUSA

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