Previously known algorithms to compute the symmetry group of a cuspedhyperbolic three-manifold and to test whether two cusped hyperbolicthree-manifolds are isometric do not apply directly to closedmanifolds. But by drilling out geodesics from closed manifolds onemay compute their symmetry groups and test for isometries using thecusped manifold techniques. To do so, one must know precisely howmany geodesics of a given length the closed manifold has. Here weprove the propositions needed to rigorously compute a length spectrum,with multiplicities. We also tabulate the symmetry groups of thesmallest known closed hyperbolic three-manifolds.
"Symmetries, isometries and length spectra of closed hyperbolic three-manifolds." Experiment. Math. 3 (4) 261 - 274, 1994.