The name Taube surface is used by Hauser for the quintic surface
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Its German name means "dove." The defining polynomial is the polynomial discriminant of 
with respect to 
.
The real parametrized surface associated with the swallowtail catastrophe lies on the Taube surface and corresponds to quartics
with a repeated real polynomial root. The real
zero set of the implicit equation also contains points
absent from that parametrized image. For example, 
gives the quartic
equation 
,
whose repeated roots are nonreal.
