2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/112987In this paper, we show that the boundary $\partialΣ(W,S)$ of a right-angled Coxeter system $(W,S)$ is minimal if and only if $W_{\tilde{S}}$ is irreducible, where $W_{\tilde{S}}$ is the minimum parabolic subgroup of finite index in $W$. We also provide several applications and remarks. In particular, we obtain that for a right-angled Coxeter system $(W,S)$, the set $\{w^{\infty} | w\in W, o(w)=\infty\}$ is dense in the boundary $\partialΣ(W,S)$.Group TheoryGeometric Topology57M07, 20F65, 20F55text