Before revision:  We provide results on topological properties of these, as well as computational experiments which show that these can often be used to reduce the number of high-dimensional simplices included in Cech filtrations  and so speed up the computation of persistent homology .
After revision:  We provide results on topological properties of these, as well as computational experiments which show that these can often be used to reduce the number of simplices included in Cech filtrations and so speed up the computation of persistent homology .