Here is a a surface of degree 6 (a
sextic)
in projective three-space
that has 65 nodes.
It was discovered by
W. Barth
in 1996.
The amazing fact here is that
a sextic can never have
more
than 65 nodes
--
so Barth's
sextic is really an extreme case.
It is in fact
the first known example of this kind.
Look into the paper
-
Barth, W.:
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
equation.
The nice computer picture shown above was made by
Stephan Endrass
using his program
SURF.
(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.