  In 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.
