Let $P$ be a compact convex polyhedron in $\mathbb{H}^3$. Let $G$ be a group generated by side-pairing isometries of $P$. Is there an algorithm to find the rank of $G$?



Rank of a group generated by side-pairing isometries of a polyhedron
I assume that you want $P$ to be a fundamental domain for $G$. Then the answer is positive, see:


I. Kapovich, R. Weidmann, Kleinian groups and the rank problem. Geom. Topol. 9 (2005), 375-402.


