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@DaniilRudenko: Some similar (here, I don't say equivalent!) formulas in the hyperbolic case were obtained by Mednykha and Pashkevich in "Elementary formulas for a hyperbolic tetrahedron" (Sib. Math. J, 2006). Especially Theorem 2 and Theorem 4 can be kind of close.
@RyanBudney: great info! Apparently it's different in SnapPea (or may be I misunderstood the C code -- that's highly possible my mistake). Thanks again!
@RyanBudney: Another (may be stupid) question: if N is a non-orientable triangulation, and M is its orientation cover, how are the pre-images of tetrahedron i in N numbered in M? 2*i - 1 and 2*i? Or it's a more complicated numbering? Having such things traceable would be extremely helpful even without more advanced functions, when it comes to see quotients of manifolds by their symmetries, etc, I think.
@RyanBudney: Hi Ryan, thanks for your reply. In Regina, however, can I also see the action of those isomorphisms on the cusps? The finicky thing is that I need to see both :-P
