  We study the metric corresponding to a three-dimensional coset space
$SO(4)/SO(3)$ in the lattice setting. With the use of three integers $n_1,
n_2$, and $n_3$, and a length scale, $l_{\mu}$, the continuous metric is
transformed into a discrete space. The numerical outcomes are compared with the
continuous ones. The singularity of the black hole is explored and different
domains are studied.
