2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/153138We consider a simplicial complex generaliztion of a result of Billera and Meyers that every nonshellable poset contains the smallest nonshellable poset as an induced subposet. We prove that every nonshellable $2$-dimensional simplicial complex contains a nonshellable induced subcomplex with less than $8$ vertices. We also establish CL-shellability of interval orders and as a consequence obtain a formula for the Betti numbers of any interval order.Combinatoricstext