  Equations of state for a cold neutron star's interior are presented in
three-column tables that relate the baryonic density, the energy density, and
the pressure. A few analytical expressions for those tables have been
established these past two decades, as a convenient way to present a large
number of nuclear models for neutron star matter. Some of those analytical
representations are based on nonunified equations of state, in the sense that
the high and the low density part of the star are not computed with the same
nuclear model. Fits of equations of state based on a piecewise polytropic
representation are revised by using unified tables of equations of state, that
is to say models which have been calculated consistently for the core and the
crust. A set of 52 unified equations of state is chosen. Each one is divided in
seven polytropes via an adaptive segmentation, and two parameters per polytrope
are fitted to the tabulated equation of state. The total mass, radius, tidal
deformability and moment of inertia of neutron stars are modelled from the fits
and compared with the quantities calculated from the original tables to ensure
the accuracy of the fits on macroscopic parameters. We provide the polytropes
parameters for 15 nucleonic relativistic mean field models, seven hyperonic
relativistic mean field models, five hybrid relativistic mean-field models, 24
nucleonic Skyrme models, and one ab initio model. The fit error on the
macroscopic parameters of neutron stars is small and well within the estimated
measurement accuracy from current and next generation telescopes.
