Volume 14, issue 3 (2010)

From the hyperbolic $24$–cell to the cuboctahedron
 1 J W Anderson, A brief survey of the deformation theory of Kleinian groups, from: "The Epstein birthday schrift" (editors I Rivin, C Rourke, C Series), Geom. Topol. Monogr. 1 (1998) 23 MR1668327 2 E M Andreev, Convex polyhedra of finite volume in Lobačevskiĭspace, Mat. Sb. $($N.S.$)$ 83 (125) (1970) 256 MR0273510 3 M Boileau, B Leeb, J Porti, Geometrization of $3$–dimensional orbifolds, Ann. of Math. $(2)$ 162 (2005) 195 MR2178962 4 A Borel, Introduction aux groupes arithmétiques, Publ. Institut Math. Univ. Strasbourg, XV. Actualités Sci. Ind. 1341, Hermann (1969) 125 MR0244260 5 B H Bowditch, Geometrical finiteness for hyperbolic groups, J. Funct. Anal. 113 (1993) 245 MR1218098 6 R D Canary, On the Laplacian and the geometry of hyperbolic $3$–manifolds, J. Differential Geom. 36 (1992) 349 MR1180387 7 D Cooper, C D Hodgson, S P Kerckhoff, Three-dimensional orbifolds and cone-manifolds, MSJ Memoirs 5, Math. Soc. Japan (2000) MR1778789 8 H S M Coxeter, Twelve geometric essays, Southern Illinois Univ. Press (1968) MR0310745 9 H S M Coxeter, Regular polytopes, Dover (1973) MR0370327 10 H S M Coxeter, Regular complex polytopes, Cambridge Univ. Press (1991) MR1119304 11 H Garland, M S Raghunathan, Fundamental domains for lattices in (R-)rank $1$ semisimple Lie groups, Ann. of Math. $(2)$ 92 (1970) 279 MR0267041 12 P de la Harpe, An invitation to Coxeter groups, from: "Group theory from a geometrical viewpoint (Trieste, 1990)" (editors É Ghys, A Haefliger, A Verjovsky), World Sci. Publ. (1991) 193 MR1170367 13 G D Mostow, Strong rigidity of locally symmetric spaces, Annals Math. Studies 78, Princeton Univ. Press (1973) MR0385004 14 G Prasad, Strong rigidity of $\mathbf{Q}$–rank $1$ lattices, Invent. Math. 21 (1973) 255 MR0385005 15 M S Raghunathan, Discrete subgroups of Lie groups, Ergebnisse Math. ihrer Grenzgebiete 68, Springer (1972) MR0507234 16 A Selberg, On discontinuous groups in higher-dimensional symmetric spaces, from: "Contributions to function theory (Internat. Colloq. Function Theory, Bombay, 1960)", Tata Inst. (1960) 147 MR0130324 17 W P Thurston, The geometry and topology of three-manifolds, Princeton Univ. Math. Dept. Lecture Notes (1979) 18 E B Vinberg, On groups of unit elements of certain quadratic forms, Math. USSR Sbornik 16 (1972) 17 19 E B Vinberg, O V Shvartsman, Discrete groups of motions of spaces of constant curvature, from: "Geometry, II", Ency. Math. Sci. 29, Springer (1993) 139 MR1254933 20 H C Wang, Topics on totally discontinuous groups, from: "Symmetric spaces (Short Courses, Washington Univ., St. Louis, Mo., 1969–1970)" (editors W M Boothby, G L and Weiss), Pure and Appl. Math. 8, Dekker (1972) 459 MR0414787 21 A Weil, On discrete subgroups of Lie groups. II, Ann. of Math. $(2)$ 75 (1962) 578 MR0137793 22 A Weil, Remarks on the cohomology of groups, Ann. of Math. $(2)$ 80 (1964) 149 MR0169956 23 D Witte Morris, Introduction to arithmetic groups, Preprint (2003)