2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/117936In this paper we construct a model for the classifying space, BVCG, of a crystallographic group G of rank n relative to the family VC of virtually-cyclic subgroups of G. The model is used to show that there exists no other model for the virtually-cyclic classifying space of G with dimension less than vcd(G)+1, where vcd(G) denotes the virtual cohomological dimension of G. In addition, the dimension of our construction realizes this limit.10 pagesAlgebraic Topology55R35 (primary); 55R40 (secondary)text