  The Zipoy-Voorhees family of static, axisymmetric vacuum solutions forms an
interesting family in that it contains the Schwarzschild black hole excepting
which all other members have naked singularity. We analyze some properties of
the region near singularity by studying a natural family of 2-surfaces. We
establish that these have the topology of the 2-sphere by an application of the
Gauss-Bonnet theorem. By computing the area, we establish that the singular
region is `point-like'. Isometric embedding of these surfaces in the three
dimensional Euclidean space is used to distinguish the two types of deviations
from spherical symmetry.
