The quaste surface is the nonic surface
![A^3+27y^4(2z+1)-54y^2z(z+1)[z^2+2x^2(2z+1)]=0,](/images/equations/QuasteSurface/NumberedEquation1.svg) |
(1)
|
where 
(Real Sociedad Matemática Española 2011, p. 31). The German name
Quaste means "tassel." The figure shows the real image of the polynomial
map below. Hauser (2006, p. 28) constructs this image by projecting a Cartesian product of a nodal
cubic and a semicubical parabola into
three-dimensional space. The polynomial map
 |  |  |
(2)
|
 |  |  |
(3)
|
 |  |  |
(4)
|
obtained by adding the second coordinates of the two curves, takes values on the quaste surface.
For real 
and 
,
the image satisfies 
.
The real zero set of the implicit equation is larger:
for example, it also contains the points with 
, 
, and 
. Thus the polynomial
map does not parametrize every real point of the implicit algebraic
surface.
