ON HYPERBOLIC 3-MANIFOLDS WITH SYMMETRIC HEEGAARD SPLITTINGS Kim, Soo-Hwan; Kim, Yang-Kok;
We construct a family of hyperbolic 3-manifolds by pairwise identifications of faces in the boundary of certain polyhedral 3-balls and prove that all these manifolds are cyclic branched coverings of the 3-sphere over certain family of links with two components. These extend some results from  and  concerning with the branched coverings of the whitehead link.
J. S. Birman and H. M. Hilden, Heegaard splittings of branched coverings of S3, Trans. Amer. Math. Soc. 213 (1975), 315-352.
J. Bracho and L. Montejano, The combinatorics of colored triangulations of manifolds, Geom. Dedicata 22 (1987), no. 3, 303-328.
A. Cavicchioli, F. Hegenbarth, and A. C. Kim, A geometric study of Sieradski groups, Algebra Colloq. 5 (1998), no. 2, 203-217.
A. Cavicchioli, F. Hegenbarth, and A. C. Kim, On cyclic branched coverings of torus knots, J. Geom. 64 (1999), no. 1-2, 55-66.
A. Cavicchioli and L. Paoluzzi, On certain classes of hyperbolic 3-manifolds, Manuscripta Math. 101 (2000), no. 4, 457-494.
M. Ferri, Crystallisations of 2-fold branched coverings of $S^3$, Proc. Amer. Math. Soc. 73 (1979), no. 2, 271-276.
M. Ferri and C. Gagliardi, Crystallisation moves, Pacific J. Math. 100 (1982), no. 1, 85-103.
M. Ferri, C. Gagliardi, and L. Grasselli, A graph-theoretical representation of PLmanifolds-a survey on crystallizations, Aequationes Math. 31 (1986), no. 2-3, 121-141.
C. Gagliardi, A combinatorial characterization of 3-manifold crystallizations, Boll. Un. Mat. Ital. A (5) 16 (1979), no. 3, 441-449.
H. Helling, A. C. Kim, and J. L. Mennicke, Some honey-combs in hyperbolic 3-space, Comm. Algebra 23 (1995), no. 14, 5169-5206.
H. Helling, A. C. Kim, and J. L. Mennicke, A geometric study of Fibonacci groups, J. Lie Theory 8 (1998), no. 1, 1-23.
H. M. Hilden, M. T. Lozano, and J. M. Montesinos-Amilibia, The arithmeticity of the figure eight knot orbifolds, Topology '90 (Columbus, OH, 1990), 169-183, Ohio State Univ. Math. Res. Inst. Publ., 1, de Gruyter, Berlin, 1992.
Y. H. Im and S. H. Kim, Heegaard splittings of the Brieskorn homology spheres that are equivalent after one stabilization, Note Mat. 20 (2001), no. 1, 53-63.
S. L. Lins and A. Mandel, Graph-encoded 3-manifolds, Discrete Math. 57 (1985), no. 3, 261-284.
L. Paoluzzi and B. Zimmermann, On a class of hyperbolic 3-manifolds and groups with one defining relation, Geom. Dedicata 60 (1996), no. 2, 113-123.
H. J. Song, Y. H. Im, and K. H. Ko, LCG moves in crystallizations, Geom. Dedicata 76 (1999), no. 3, 229-251.
W. P. Thurston, The Geometry and Topology of 3-Manifolds, Lect. Notes, Princeton, N.J., Princeton Univ. Press, 1980.