Co-Seifert fibrations of compact flat 3-orbifolds (Q6142726)

An \(n\)-dimensional crystallographic group (\(n\)-space group) is the fundamental group of a compact flat \(n\)-orbifold. A co-Seifert fibration of a flat \(n\)-orbifold \(M\) is a surjective map from \(M\) to a 1-orbifold \(B\) with totally geodesic fibers that restricts to a fiber bundle projection over the ordinary set of \(B\). In this paper as a continuation of their previous papers (in particular [the authors, Commun. Algebra 49, No. 2, 639--657 (2021; Zbl 1498.20130)]), the authors classify all the co-Seifert fibrations of compact flat 3-orbifolds up to affine equivalence, and verify Table 1 in [the authors, Algebr. Geom. Topol. 10, No. 3, 1627--1664 (2010; Zbl 1245.57026)]. The classification contains a description of the structure group actions. It is arranged by the 17 wallpaper groups (2-space groups) of generic fibers together with the IT (international tables) numbers of 3-space groups. Furthermore, the authors describe enantiomorphic (chiral) 3-space group pairs using co-Seifert fibrations.