  We study the exact solution of Einstein's field equations consisting of a
($n+2$)-dimensional static and hyperplane symmetric thick slice of matter, with
constant and positive energy density $\rho$ and thickness $d$, surrounded by
two different vacua. We explicitly write down the pressure and the external
gravitational fields in terms of $\rho$ and $d$, the pressure is positive and
bounded, presenting a maximum at an asymmetrical position. And if
$\sqrt{\rho}\,d$ is small enough, the dominant energy condition is satisfied
all over the spacetime. We find that this solution presents many interesting
features. In particular, it has an empty singular boundary in one of the vacua.
