  We study the boundary of the 3-dimensional Rauzy fractal ${\mathcal E}
\subset \RR \times \CC$ generated by the polynomial $P(x) = x^4-x^3-x^2-x-1$.
The finite automaton characterizing the boundary of ${\mathcal E}$ is given
explicitly. As a consequence we prove that the set ${\mathcal E}$ has 18
neighborhoods where 6 of them intersect the central tile ${\mathcal E}$ in a
point. Our construction shows that the boundary is generated by an iterated
function system starting with 2 compact sets.
