Geodesic
Hyperbolic 3-Manifolds with Geodesic Boundary: Enumeration and Volume Calculation
Informatics and Automation, Geometric topology, discrete geometry, and set theory, Tome 252 (2006), pp. 167-183

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We describe a natural strategy to enumerate compact hyperbolic 3-manifolds with geodesic boundary in increasing order of complexity. We show that the same strategy can be applied in order to analyze simultaneously compact manifolds and finite-volume manifolds with toric cusps. In contrast, we show that if one allows annular cusps, the number of manifolds grows very rapidly and our strategy cannot be employed to obtain a complete list. We also carefully describe how to compute the volume of our manifolds, discussing formulas for the volume of a tetrahedron with generic dihedral angles in a hyperbolic space. 
@article{TRSPY_2006_252_a14,
     author = {A. D. Mednykh and C. Petronio},
     title = {Hyperbolic {3-Manifolds} with {Geodesic} {Boundary:} {Enumeration} and {Volume} {Calculation}},
     journal = {Informatics and Automation},
     pages = {167--183},
     publisher = {mathdoc},
     volume = {252},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2006_252_a14/}
}
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A. D. Mednykh; C. Petronio. Hyperbolic 3-Manifolds with Geodesic Boundary: Enumeration and Volume Calculation. Informatics and Automation, Geometric topology, discrete geometry, and set theory, Tome 252 (2006), pp. 167-183. http://geodesic.mathdoc.fr/item/TRSPY_2006_252_a14/