(2.2.4) For every $dlt$-model $\mathscr{X}$ of $X$, the log canonical centers of $(\mathscr{X},(\mathscr{X}_{s})_{\mathrm{red}})$ are the irreducible components of intersections of irreducible components of $(\mathscr{X}_{s})_{\mathrm{red}}$, by [Ko13, 4.16]. These are also precisely the closures in $\mathscr{X}_{s}$ of the connected components of intersections of irreducible components of $\mathscr{X}^{\mathrm{snc}}_{s}$ (since these connected components are the log canonical centers of $(\mathscr{X}^{\mathrm{snc}},(\mathscr{X}_{s}^{\mathrm{snc}})_{\mathrm{red}})$). Thus, the dual intersection complex $\mathcal{D}((\mathscr{X}_{s})_{\mathrm{red}})$ is the same as the dual intersection complex of the strict normal crossings divisor $\mathscr{X}^{\mathrm{snc}}_{s}$, and the cells of this complex correspond bijectively to the log canonical centers of $(\mathscr{X},(\mathscr{X}_{s})_{\mathrm{red}})$. See Section 2 in [dFKX12] for more background.