[Cos-top] hyperbolic 3D spaces with cubical FDs?

hi cos-top Do there exist any hyperbolic multiply connected constant-curvature compact spaces for which the fundamental domain is a cube (with flat faces, of course) for some points in the space? Or is there a proof that this is impossible? We know that there are (at least) two such spherical spaces, that Peter Kramer calls C_2 and C_3: Kramer09: https://ui.adsabs.harvard.edu/#abs/2009PhyS...80b5902K/ Are there any hyperbolic ones? Cheers Boud [Reminder - this is an opt-in list - you can get info at http://cosmo.torun.pl/mailman/listinfo/cos-top for unsubscribing or subscribing; information should be included in this email for doing these or other operations via email.]