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Tetranoid

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finite numerical model of a tetranoid

The name tetranoid is used in the IMAGINARY exhibition for a constant mean curvature surface with four ends and tetrahedral symmetry. It is obtained by an immersion of a Riemann sphere with four points removed into three-dimensional Euclidean space. Its mean curvature is nonzero.

Schmitt (2007, pp. 11 and 15) constructed families of these surfaces using the Dorfmeister-Pedit-Wu method. The Riemann sphere supplies a genus zero domain, with each removed point corresponding to an end. The figure shows a finite numerical model from the jReality example data.

See also

Constant Mean Curvature Surface, Dorfmeister-Pedit-Wu Method, Tetrahedral Group

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References

IMAGINARY. "Ulrich Pinkall, Nicholas Schmitt, Charles Gunn and Tim Hoffmann." https://www.imaginary.org/gallery/ulrich-pinkall-nicholas-schmitt-charles-gunn-and-tim-hoffmann.jReality. "Example 3D Data: Tetranoid." https://www3.math.tu-berlin.de/jreality/jrealityStatic/ws/data/vrExamples.jar.Schmitt, N. "Constant Mean Curvature n-Noids with Platonic Symmetries." 15 Feb 2007. https://arxiv.org/abs/math/0702469.

Cite this as:

Weisstein, Eric W. "Tetranoid." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Tetranoid.html

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