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Schwarz CLP Surfaces


SchwarzCLPSurfaces

Schwarz CLP surfaces are a two-parameter family of triply periodic minimal surfaces, up to scaling, obtained by continuing a solution of Plateau's problem bounded by six edges on two faces of a rectangular box. Half-turn rotations about the straight boundary edges extend the patch to a periodic minimal surface (Schwarz 1871, Weber).

The designation CLP means "crossed layers of parallels." The geometry resembles two perpendicular systems of parallel layers joined by alternating tunnels (Brakke, Weber). The figure shows a numerically sampled finite patch of a representative in Weber's construction.

The conjugate minimal surfaces are also triply periodic. They are sometimes included under the same CLP name, although a general member need not be congruent to its conjugate (Weber).


See also

Conjugate Minimal Surface, Minimal Surface, Schwarz Surfaces, Triply Periodic Minimal Surface

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References

Brakke, K. "Triply Periodic Minimal Surfaces." https://kenbrakke.com/evolver/examples/periodic/periodic.html.Schwarz, H. A. Bestimmung einer speciellen Minimalfläche. Eine von der Königlichen Akademie der Wissenschaften zu Berlin am 4. Juli 1867 gekrönte Preisschrift. Nebst einem Nachtrage, einem Anhange und 6 Figurentafeln. Berlin, Germany: W. Vogt, 1871. https://gdz.sub.uni-goettingen.de/id/PPN309770653.Weber, M. "Schwarz CLP-Surfaces." https://minimalsurfaces.blog/home/repository/triply-periodic/schwarz-clp-surfaces/.

Cite this as:

Weisstein, Eric W. "Schwarz CLP Surfaces." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SchwarzCLPSurfaces.html

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