Here is a a surface of degree 6 (a sextic
in projective three-space
that has 65 nodes.
It was discovered by
The amazing fact here is that
a sextic can never have
than 65 nodes
sextic is really an extreme case.
It is in fact
the first known example of this kind.
Look into the paper
Two projective surfaces with many nodes, admitting the symmetries of the icosahedron.
J. Algebraic Geometry 5, 173-186 (1996)
to learn about the construction of the surface and its
The nice computer picture shown above was made by
using his program
(SURF can draw pictures
of a surface in three-space
when you provide an equation of the surface.)
If you are interested in a classical surface, don't forget to
have a look at
Clebsch's diagonal cubic.