Fibered orbifolds and crystallographic groups, II

Understand

Let G be an n-dimensional crystallographic group (n-space group).

• If G is a Z-reducible, then the flat n-orbifold E^n/G has a nontrivial fibered orbifold structure.
• We prove that this structure can be described by a generalized Calabi construction, that is, E^n/G is represented as the quotient of the Cartesian product of two flat orbifolds under the diagonal action of a structure group of isometries.
• We determine the structure group and prove that it is finite if and only if the fibered orbifold structure has an orthogonally dual fibered orbifold structure.