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Cube Surface

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CubeSurface

The name cube surface is used by Hauser for the sextic surface

x^6+y^6+z^6=1.

It is the supersphere with radius 1 and exponent 6, or equivalently a superellipsoid with all three semiaxes equal to 1 and both exponents equal to 1/3. The surface is smooth and is unchanged by permuting the coordinates or reversing their signs. The supersphere with radius 1 and exponent 4 is the "rounded cube" special case of Goursat's surface.

See also

Goursat's Surface, Sextic Surface, Superellipsoid, Supersphere

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References

Hauser, H. "Gallery of Singular Algebraic Surfaces: Cube." https://homepage.univie.ac.at/herwig.hauser/gallery.html.

Cite this as:

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

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