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In this paper we address some problems concerning an approximate Dirichletdomain. We show that under some assumptions the approximate Dirichlet domaincan work equally well as an exact Dirichlet domain. In particular, we considera problem of tiling a hyperbolic ball with copies of the Dirichlet domain. Thisproblem arises in the construction of the length spectrum algorithm which isim- plemented by the computer program SnapPea. Our result explains theempirical fact that the program works surprisingly well despite it does not useexact data. Also we demonstrate an improvement in the algorithm for rigorousconstruction of the length spectrum of a hyperbolic 3-manifold.

Rigorous computations with an approximate Dirichlet domain