TITLE: Do you know how to construct a compact hyperbolic 3-manifold with three or four totally geodesic boundary components?
QUESTION [6 upvotes]: Do you know how to construct a compact hyperbolic 3-manifold with three or four totally geodesic boundary components?  The only constructions I could find have one boundary component.  A reference would be appreciated.

REPLY [9 votes]: A beautiful construction (relying on 2-dimensional hyperbolic circle packings) of hyperbolic 3-manifolds with many totally geodesic boundary components can be found in the paper
Totally geodesic boundaries are dense in the moduli space.
J. Math. Soc. Japan 49 (1997), no. 3, 589--601.
by Fujii and Soma.