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References

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2. A. Borel, Commensurability classes and volumes of hyperbolic 3-manifolds, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4)8(1981), no. 1, 1–33.

3. A. Borel, Harish-Chandra, Arithmetic subgroups of algebraic groups, Ann. of Math. (2)75(1962) 485–535.

4. H. M. Hilden, M. T. Lozano, J. M. Montesinos-Amilibia, On the Borromean orbifolds: geometry and arithmetic,Topology ’90 (Columbus, OH, 1990), 133–

167, Ohio State Univ. Math. Res. Inst. Publ., 1, de Gruyter, Berlin, 1992.

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ò

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4÷ @™=?>?öÏò&ºK»½¼¿¾NÀ B

ðÂÁ˜Ã-ĭœðÇÆ0È

É ð 1999^Ê

4ÌË É ð 1993^Ê

B

.

6. C. Maclachlan, A. W. Reid, Commensurability classes of arithmetic Kleinian groups and their Fuchsian subgroups, Math. Proc. Cambridge Philos. Soc.102 (1987), no. 2, 251–257.

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8. C. Maclachlan, A. W. Reid, Invariant trace-fields and quaternion algebras of polyhedral groups, J. London Math. Soc. (2)58(1998), no. 3, 709–722.

9. A. W. Reid, Arithmetic Kleinian groups and their Fuchsian subgroups, Ph.D¿

Thesis (1987), University of Aberdeen.

10. A. W. Reid, A non-Haken hyperbolic 3-manifold covered by a surface bundle, Pacific J. Math.167(1995), no. 1, 163–182.

11. P. Scott, Subgroups of surface groups are almost geometric, J. London Math.

Soc. (2) 17 (1978), no. 3, 555–565. Correction: J. London Math. Soc. (2) 32 (1985), no. 2, 217–220.

4 þ ÿ

12. `E. B. Vinberg, Discrete groups generated by reflections in Lobaˇcevski˘i spaces, Math. USSR-Sbornik1(1967), no. 3, 429–444.

13. H. Yoshida, Invariant trace fields and commensurability of hyperbolic 3- manifolds, KNOTS ’96 (Tokyo), 309–318, World Sci. Publishing, River Edge, NJ, 1997.

Figure 1. A right-angled regular truncated icosahedron in the Poincar´e ball model of H³