In this paper, we prove that a normal subgroup of an –dimensional crystallographic group determines a geometric fibered orbifold structure on the flat orbifold , and conversely every geometric fibered orbifold structure on is determined by a normal subgroup of . In particular, we prove that is a fiber bundle, with totally geodesic fibers, over a –dimensional torus, where is the first Betti number of .
"Fibered orbifolds and crystallographic groups." Algebr. Geom. Topol. 10 (3) 1627 - 1664, 2010. https://doi.org/10.2140/agt.2010.10.1627