  We continue investigations started by Lakeland on Fuchsian and Kleinian
groups which have a Dirichlet fundamental domain that also is a Ford domain in
the upper half-space model of hyperbolic $2$- and $3$-space, or which have a
Dirichlet domain with multiple centers. Such domains are called DF-domains and
Double Dirichlet domains respectively. Making use of earlier obtained concrete
formulas for the bisectors defining the Dirichlet domain of center $i \in
\HQ^2$ or center $j \in \HQ^3$, we obtain a simple condition on the matrix
entries of the side-pairing transformations of the fundamental domain of a
Fuchsian or Kleinian group to be a DF-domain. Using the same methods, we also
complement a result of Lakeland stating that a cofinite Fuchsian group has a DF
domain (or a Dirichlet domain with multiple centers) if and only if it is an
index $2$ subgroup of the discrete group G of reflections in a hyperbolic
polygon.
