  We investigate the properties of a closed-form analytic solution recently
found by Manko et al. (2000) for the exterior spacetime of rapidly rotating
neutron stars. For selected equations of state we numerically solve the full
Einstein equations to determine the neutron star spacetime along constant rest
mass sequences. The analytic solution is then matched to the numerical
solutions by imposing the condition that the quadrupole moment of the numerical
and analytic spacetimes be the same. For the analytic solution we consider,
such a matching condition can be satisfied only for very rapidly rotating
stars. When solutions to the matching condition exist, they belong to one of
two branches. For one branch the current octupole moment of the analytic
solution is very close to the current octupole moment of the numerical
spacetime; the other branch is more similar to the Kerr solution. We present an
extensive comparison of the radii of innermost stable circular orbits (ISCOs)
obtained with a) the analytic solution, b) the Kerr metric, c) an analytic
series expansion derived by Shibata and Sasaki (1998) and d) a highly accurate
numerical code. In most cases where a corotating ISCO exists, the analytic
solution has an accuracy consistently better than the Shibata-Sasaki expansion.
The numerical code is used for tabulating the mass-quadrupole and
current-octupole moments for several sequences of constant rest mass.
