The Herz surface is the quartic surface
named by Hauser. Its German name means "heart" (Real Sociedad Matemática Española 2011, p. 67). Its singular points
form the 
-axis.
The cross section by the plane 
consists of this axis
and the circle
Near the origin, the polynomial map 
is an invertible change of coordinates taking the Herz surface to the kolibri
surface 
.
The sextic heart surfaces have different defining
equations.
See also
Heart Surface,
Kolibri
Surface,
Quartic Surface
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References
Hauser, H. "Gallery of Singular Algebraic Surfaces: Herz." 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. 67, 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. "Herz Surface." From
MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HerzSurface.html
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