  We provide a way of representing a four dimensional regular black hole
geometry at the black string style. We enunciate a list of constrains in order
to that the complete five dimensional geometry to be regular. Following these
constraints were constructed both the four and the five dimensional geometries.
  The assumptions used to solve the equations of motion suggest a relation
between the $4D$ and the $5D$ Newton constants, which coincides with relations
previously showed in the literature. Furthermore, the $(\mu,\nu)$ components of
the five dimensional equations of motion adopt the form of the four dimensional
equations of motion. Also, the five dimensional conservation equation adopts
the form of the four dimensional conservation equation.
  At the origin the topology of the five dimensional geometry corresponds to
the product between the four dimensional de--Sitter space--time and $S^1$ with
$z$ compact. This latter differs from the Kaluza-Klein black string, where, at
the origin the topology corresponds to the product between the Schwarzschild
singularity and $R(S^1)$ for $z$ non compact (compact). The topology of the
complete five dimensional geometry corresponds to $S^2 \times S^1$. At the
infinity of the radial coordinate the topology corresponds to the product
between Minkowski and $S^1$.
  At the induced four dimensional geometry we compute the first law of
thermodynamics with the correct values of temperature and entropy.
