  We determine explicit formulas for the bisectors used in constructing a
Dirichlet fundamental domain in hyperbolic two and three space. They are
compared with the isometric spheres employed in the construction of a Ford
domain and used to find a finite set of generators for discrete groups of
finite covolume. Applications are given to Fuchsian groups, Kleinian groups,
including the Bianchi groups, and for the construction of a finite set of
generators of the unit group of the integral group ring of a finite nilpotent
group. An easy implementable algorithm, DAFC, is also given and used in the
search for generators of discrete groups.
