Generalize the Schwarz reflection principle for non-reflection wallpaper groups
Establish a generalized Schwarz reflection principle applicable to wallpaper symmetry groups that lack reflections (for example, the group 2222), and prove that it yields a unique conformal hyperbolization by enabling analytic continuation across fundamental domain boundaries via symmetry operations.
References
Nevertheless, it appears that a suitable generalization of the SRP can produce a unique conformal hyperbolization in this setting. Although no formal proof exists so far, numerical evidence looks promising.
— The Smooth Power of the "Neandertal Method"
(Montag et al., 10 Jul 2025) in Subsection '2222 and 0' (Section 'The Lower Symmetry Groups')