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Algebraic Surfaces with Many Nodes

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equation
Togliatti quintic (31 nodes)
range
opacity
recursion
0
1
2
3
style
color
texture
region
cube
sphere
An algebraic surface is defined as the set of points
(x,y,z)
that satisfy a polynomial equation
f(x,y,z)=0
. An ordinary double point (or node) is a point where the surface intersects itself and satisfies
f=
f
x
=
f
y
=
f
z
=0
. The maximum possible number of nodes is a function of the degree of
f
.
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