2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/165399We 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.19 pagesNumber TheoryCombinatorics11B85text