The Eistüte surface is the sextic surface
named by Hauser. Its German name means "ice-cream cone" (Real Sociedad Matemática Española 2011, p. 63). Its singular
points form the 
-axis.
The cross section by a horizontal plane 
is a four-leaved rose
curve. In polar coordinates its equation
is
Thus all horizontal cross sections have the same shape, scaled by 
.
See also
Rose Curve,
Sextic
Surface
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References
Hauser, H. "Gallery of Singular Algebraic Surfaces: Eistüte." 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. 63, 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. "Eistüte Surface."
From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/EistuteSurface.html
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