  We conduct a direct comparison of three different representative numerical
codes for constructing models of rapidly rotating neutron stars in general
relativity. Our aim is to evaluate the accuracy of the codes and to investigate
how the accuracy is affected by the choice of interpolation, domain of
integration and equation of state. In all three codes, the same physical
parameters, equations of state and interpolation method are used. We construct
25 selected models for polytropic equations of state and 22 models with
realistic neutron star matter equations of state. The three codes agree well
with each other (typical agreement is better than 0.1% to 0.01%) for most
models, except for the extreme assumption of uniform density stars. We conclude
that the codes can be used for the construction of highly accurate initial data
configurations for polytropes of index N > 0.5 (which typically correspond to
realistic neutron stars), when the domain of integration includes all space and
for realistic equations with no phase transitions. With the exception of the
uniform density case, the obtained values of physical parameters for the models
considered in this paper can be regarded as ``standard'' and we display them in
detail for all models.
