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Nordstrand's Weird Surface


Nordstrand's weird surface

"Nordstrand's weird surface" is an attractive quartic surface given by the implicit equation

 25[x^3(y+z)+y^3(x+z)+z^3(x+y)]+50(x^2y^2+x^2z^2+y^2z^2)-125(x^2yz+y^2xz+z^2xy)+60xyz-4(xy+xz+yz)=0.

It has 11 ordinary double points located at (2/5,0,0), (-2/5,0,0), (-2/15,2/15,2/15), (0,0,-2/5), (0,0,2/5), (0,2/5,0), (0,-2/5,0), (2/5,2/5,2/5), (2/15,2/15,-2/15), (2/15,-2/15,2/15), and (0,0,0).


See also

Quartic Surface

Explore with Wolfram|Alpha

References

Nordstrand, T. "Weird Cube." http://jalape.no/math/weirdtxt.

Cite this as:

Weisstein, Eric W. "Nordstrand's Weird Surface." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/NordstrandsWeirdSurface.html

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