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Kreisel Surface

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kreisel surface with its singular equatorial circle and poles marked in orange

The Kreisel surface is the sextic surface

60(x^2+y^2)z^4=(60-x^2-y^2-z^2)^3,

named by Hauser. Its German name means "spinning top" (Real Sociedad Matemática Española 2011, p. 57). It is a surface of revolution about the z-axis and is invariant under reflection in the xy-plane. Every real point satisfies x^2+y^2+z^2<=60, so the surface is bounded.

Its real singular points form the equatorial circle z=0, x^2+y^2=60 together with the two poles (0,0,+/-sqrt(60)).

See also

Sextic Surface, Surface of Revolution

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References

Hauser, H. "Gallery of Singular Algebraic Surfaces: Kreisel." https://homepage.univie.ac.at/herwig.hauser/gallery.html.Real Sociedad Matemática Española. RSME-IMAGINARY: Una mirada matemática. Madrid, Spain: Real Sociedad Matemática Española, p. 57, 2011. https://fme.upc.edu/ca/exposicio-imaginary-una-simfonia-matematica-fme-2021/material-docemt/rsmeimaginary_catalogue_es.pdf.

Cite this as:

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

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