Obstructions to shellability

We consider a simplicial complex generalization of a result of Billera and Myers that every nonshellable poser contains the smallest nonshellable poset as an induced subposet. We prove that every nonshellable two-dimensional simplicial complex contains a nonshellable induced subcomplex with less than eight vertices. We also establish CL-shellability of interval orders and as a consequence obtain a formula for the Betti numbers of any interval order.