Limit volumes of hyperbolic three-orbifolds (Q911108)

We prove that the smallest three limit volumes for hyperbolic 3-orbifolds are 0.3053218..., 0.4444514... and 0.4579827.... The corresponding unique orbifolds are given. We also show that an n-fold limit point of volumes of hyperbolic 3-orbifolds is bounded below by (n-1/2)(v/2) where \(v=1.01494..\). is the volume of an ideal regular tetrahedron in hyperbolic 3-space. Applications to the order of the isometry groups of hyperbolic 3-manifolds are also given.