Let $P$ be a compact convex polyhedron in $\mathbb{H}^3$. Let $G$ be a group generated by sidepairing isometries of $P$. Is there an algorithm to find the rank of $G$?
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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), 375402. 

