  We present a new method for Monte Carlo or Molecular Dynamics numerical
simulations of three dimensional polar fluids. The simulation cell is defined
to be the surface of the northern hemisphere of a four-dimensional
(hyper)sphere. The point dipoles are constrained to remain tangent to the
sphere and their interactions are derived from the basic laws of electrostatics
in this geometry. The dipole-dipole potential has two singularities which
correspond to the following boundary conditions : when a dipole leaves the
northern hemisphere at some point of the equator, it reappears at the antipodal
point bearing the same dipole moment. We derive all the formal expressions
needed to obtain the thermodynamic and structural properties of a polar liquid
at thermal equilibrium in actual numerical simulation. We notably establish the
expression of the static dielectric constant of the fluid as well as the
behavior of the pair correlation at large distances. We report and discuss the
results of extensive numerical Monte Carlo simulations for two reference states
of a fluid of dipolar hard spheres and compare these results with previous
methods with a special emphasis on finite size effects.
